This.
I got a pair of Headwind pants last year. love them. I also have the Headwind jacket.
I carry my clothes with me every day in my pannier and change in the locker room after wiping off or showering.
If you don't have a locker room, and just an office or a bathroom, pack a lightweight camping quickdry towel or some wipes, and change where you can.
When I was riding to school (as a teacher) I changed in my classroom closet, and hung everything up to air out during the day in there too.

Well, to me it's pretty obvious that not having to change at all is the easiest approach, and it's a viable option for a number of people. It was for me for a few years.

What type of bike would do that?

Bike specific clothing happens for a few reasons:
1. Weather - needing to dress for the weather outside, rather than the controlled temps inside, so you're comfortable / healthy / safe for weather conditions.
2. Physical Flexibility - You're exercising, clothing that doesn't restrict movement.
3. Durability - needing clothing that's durable for riding with the bike. (Jeans tend to wear on the seat and wear out.)

Do you have a kind of bike in mind? One could possibly change their sense of fashion to accommodate #2 and #3 , but #1 seems like it would require an enclosure over the bike, as a well as a gas powered heater and air conditioner lol.

Lol well it's true that there are different kind of "pants". I mentioned the Shower's Pass page because I wasn't sure what level the OP needed exactly. There's:
1. Form fitting "check out my ass tights" lol. I mean hey, they're really comfortable and look fine on the bike. I just don't like walking into work with them.
2. Semi-pants that are looser than tights but still not as wide as pants. This is the category Novara Headwind pants are in. I don't have a problem walking into work in them, but I would want to sit in them at work all day, they would look out of place.
3. Full on pants. Exact same shape as regular pants. Though "wind resistance" isn't a big deal for me, it was difficult for me to find anything like this that was also windproof front, breathable, stretchy, and durable (bike jeans aren't as durable as synthetic bike gear). Not saying it's impossible, just that I was looking around and didn't see it so I bought the Novara Headwind pants instead.

It's hard for me to tell exactly what the OP is looking for, OP says they'd rather not change pants, but also doesn't want to risk chain grease on their pants, so they might need to change pants. I guess rereading it I might have mostly read the title and not read through what the OP was asking for as closely as I should have... :-/

The Showers Pass Rogue pant might be the closest I know of offhand:
https://www.showerspass.com/products/rogue-pant

https://i.ytimg.com/vi/9l7GRTbOjuM/maxresdefault.jpg

Lol well it's true that there are different kind of "pants". I mentioned the Shower's Pass page because I wasn't sure what level the OP needed exactly. There's:
1. Form fitting "check out my ass tights" lol. I mean hey, they're really comfortable and look fine on the bike. I just don't like walking into work with them.
2. Semi-pants that are looser than tights but still not as wide as pants. This is the category Novara Headwind pants are in. I don't have a problem walking into work in them, but I would want to sit in them at work all day, they would look out of place.
3. Full on pants. Exact same shape as regular pants. Though "wind resistance" isn't a big deal for me, it was difficult for me to find anything like this that was also windproof front, breathable, stretchy, and durable (bike jeans aren't as durable as synthetic bike gear). Not saying it's impossible, just that I was looking around and didn't see it so I bought the Novara Headwind pants instead.

It's hard for me to tell exactly what the OP is looking for, OP says they'd rather not change pants, but also doesn't want to risk chain grease on their pants, so they might need to change pants. I guess rereading it I might have mostly read the title and not read through what the OP was asking for as closely as I should have... :-/

The Showers Pass Rogue pant might be the closest I know of offhand:
https://www.showerspass.com/products/rogue-pant

P.S. Closer to the OP's request, "Club Ride" makes some normal looking bike pants to:
Men's Pants ? Club Ride Apparel

I'm wearing their jeans, I love them, they're very stretchy but they still look like regular jeans. In the last month I've tried on at least 10 pairs of jeans, and the "Cog" straight jeans have been the more comfortable than everything else while still looking pretty much like regular jeans:
Cog Jean ? Club Ride Apparel

They also make a more tapered jean called the "Shift" jean that I also bought and is good but haven't worn past trying on yet:
Shift Jean ? Club Ride Apparel
http://cdn.shopify.com/s/files/1/017...82356413922223

These jeans have a lot of bike-specific features (no-crack back, stretchy water resistant material, reinforced crotch), but ironically I wear them for everything except biking because they're expensive and didn't hold up that well last time I wore them on the bike. 1 ride and they were already showing signs of wear in the crotch (despite the reinforced crotch). It was an older model, so maybe they made improvements, but jean material is just not very durable when rubbing against the side of a bike seat in my experience.

Their Worx Trouser is another suggestion, the material is "denim-like" (the others are actual denim) so maybe it be more durable:
Worx Trouser ? Club Ride Apparel
http://cdn.shopify.com/s/files/1/017...98329092399383

They also make a "Fat Jack" pant that's more of a "primary biking, secondary look like regular pants" pant. Made out of polyster which I think is far more durable for biking. But the slightly different colored material across the thigh on it made me think it would look a little weird to wear at work. But who's knows, fashion taste differs from one person to another.
Fat Jack ? Club Ride Apparel
http://cdn.shopify.com/s/files/1/017...40214345474760

There's a number of suggestions that are probably closer to what the OP was looking for. Sorry, read the title but not the original post as closely as I should have...

Are you talking about these? These look like tights to me.
Novara Headwind Bike Pants - Men's - REI.com

Here's a different link:

Novara Headwind Bike Pants

http://www.rei.com/media/c31ecee2-20...b-3e9f8bdce33e

The text description:

"Are gray skies threatening to rain on your bike commute? Pull the Headwind pants on over your work pants to keep them dry and clean during the ride. Plus, they're breathable so you won't overheat. "

So you could pull these over regular works pants. Mine are a few years older and might be a bit more snug because pulling them over regular pants isn't easy, I just tried it. It can be done but they tend to pull the hems of my pant legs up over my knee. To be honest I don't think I've every tried them in the rain, I just wear them in cold weather.

Ah ok that's better :)

Carrying shoes, pants, shirt, socks, underwear - carrying all this ends up needing a pannier. Having a pannier adds wind resistance and reduces the "agile" feel of a lot of bikes. Aka it's more fun riding for some people without pannier. I have a trunk but prefer to ride with no pannier myself.

The bike just handles in a more fun way without a big block of weight on it.

I only discovered this morning, the Levi's have reflective piping inside the cuff on the outside seam, so it faces out if you roll them up. Not sure if this seems good or twee

An upright bike with fenders, and a chainguard or case. Of my 7 bikes, my Dutch Gazelle checks all the boxes.

1. There's plenty of clothing available that is suitable for all weather.
2. An upright bike accommodates most types of clothing.
3. The wider seats and riding position on upright bikes eliminate that problem.

I commute 16 miles a day in very hilly terrain year round in normal clothes. Last Saturday I rode 31 miles wearing jeans, golf shirt, pea coat, and Dr. Martin shoes.
Really the only bike specific items I find nessary are rain gear, and helmets.

I've worn them in rain a lot. They're not waterproof but definitely water resistent. A couple times I was caught in a heavy downpour and they soaked through but it took a whole.

I went for the thermal tights. No one batted an eye except for the better looking female coworkers, which I can live with. They're solid black and have the chamois padding, so they're not too revealing. And everyone knows I'm an avid cyclist, so no one cares.

I have a bike that matches that description. Technically, it would not have been necessary to commute on my bike in bike-specific clothing, even in 90 degree F summer weather with high humidity.

However, I opted to wear clothing that would improve the ride experience considerably over wearing my office clothes on a 13-mile commute under those conditions: Polyester t-shirt, mountain bike shorts, quick-dry socks.

My company uniform is basically active wear with items suitable for all weather conditions so that's an advantage, but there's not many styles of clothing short of formal wear that isn't available in materials and fit suitable for bike riding.

When commuting in uniform I do prefer to wear an active wear shirt so I can start my work day with a fresh shirt, but beyond that I don't find it necessary to change anything else. When it gets cold I wear a fleece vest or uniform sweater, and a wool or knit cap.

On my own time, I wear season appropriate active wear, causal wear, or dress clothes made of synthetics or wool, and occasionally European military surplus from thrift stores, and sources such as sportsmans guide. My most recent "cycling specific" purchases are a surplus navy pea coat and Italian army wool knickers, neither of which are limited to just cycling.

I enjoy riding my road bike when so inclined, but it comes with a lot of limitations from a practical standpoint, and I do have some cycling specific clothes to accommodate such riding. Its just not my "go to" most of the time.

I agree with the last part of your sentence. I wore non-cycling-specific clothes - jeans or office slacks, button-down shirt and cotton undershirt when I test-rode a lot of road bikes. One LBS though insisted I put on a helmet. I did end up drenched in sweat though after a summer evening test ride. I had planned to attend a concert at somebody's house afterwards, but didn't consider that it was far enough from a Metro station that I'd have to bike there. Social interaction in this sweat-drenched state was awkward.

My normal office attire is business casual slacks and button down shirt. I could commute to work by bike 13 miles each way in this attire but I prefer not to. When it is 90 F with dew point over 70, it is not possible for me to bike commute without sweating buckets, even when my average speed was below 10 mph on my upright bike. Riding my commute without sweat even during the hottest conditions might be possible if you're on an e-Bike and have the right combination of genetics.

I have coworkers who roll into work on their bikes in their office clothes with no perceptible sweat. These people live 3 miles away or closer and ride on flat terrain.

Re: bringing clothes to work. We have storage lockers at work, but I'm on a waiting list to acquire one. If I had one, I could bring my clothes and toiletries on my non-cyclocommute days and stash them in the locker. It would be nice to ride to work for once without a pannier or backpack. I guess I could stash them in my cubicle but then having to go up to my cubicle after parking my bike. Then again, I like being able to park my bike, and walk down the hall (where the lockers are) to the showers instead of taking a side trip to my cubicle. I'd rather carry a pannier/backpack down that hall than take the side trip.

I have the same pants and absolutely love them. I find I am good to about 40 degrees typical of morning winter rides here in Phoenix and when the temps dip into the 30's, I wear a base layer under them. I agree on the panniers for carrying clothes for work, which I do, but I have a pair of shoes I leave at work so I am only carrying clothes, underwear and socks. The trade off of course is performance which you loose with panniers and the extra weight, but I am not in a big rush and can make some speed if necessary and it solves the work clothing equation nicely for me.

For my 30 mi RT commute I always wear bike specific clothes. Last year tights and long sleeve baselayer were pretty much the only thing that kept me out of ER when I had a major spill. It was a choice between hitting concrete on the right or becoming a hood ornament. Massive hematomas, six months of sore shoulder and practically no road rash. Lycra is surprisingly tough. I started wearing full coverage year round, even in summer. Clean up on arrival is not all that bothersome.

I love the MEC Adanac pants for anything between 5-15°C. I only glanced quickly, but the Novara Headwind as mentioned in the above responses might be the closest comparable from REI.

I have a pair of mountain hardware hiking pants with zip off legs. I wear bike shorts underneath and underwear. I use leg straps as well. When it gets cold I will wear a pair of tights under the pants. If it gets warm, I zip off the legs. I use these same pants in the winter months even if I am on a long weekend ride. They are very comfortable, etc.

You can't get lower than 5°C with these? Makes price to °C ratio quite high (or number of days worn per year quite low).

I could...probably down to freezing, but I use thermal pants for 5°C and lower. You could also wear a base layer to use them in even colder temps.

I'd be surprised if they're not the same as the REI pants - it looks like they used the same model in the same pose! I try to avoid looking at MEC stuff because I want to buy it and it's just not economical for us in the lower states. When are they going to open a US location?!

But it's in Canadian dollars. Just mentally replace CAD by US and you shouldn't be so far off.

then add shipping to US... kaboom!