I have a Jamis Aurora. It came with 700x32 Vittoria Randonneur tires. I'm wondering if I can switch to 28c and still use the same rims? Reasons are,

1. I need a new tire and I can't find any 32's in stock anywhere, and
2. I figure 28's might be a little faster anyway...

I want to stick with the same tires unless I can't find what I want. I've only had one flat in two years, riding through all kinds of l.a. road debris, that wasn't caused by user error and the ride seems pretty grippy to me.

I changed from a 700x38 to a 700x28 on my Hybrid bike. I used Sheldon Brown guidline before swapping it. Somewhere down the article near the bottom is where he has a table showing rim size and tire recommendation.
https://sheldonbrown.com/tire-sizing.html

You do have to remove your old tire so that you can measure it. I took a guess at my thickness of the rim instead. Most rims with the original tire that came with it are usually OK to go down in tire size but going up in size is more limited.

As for speed, that is questionable. I did notice a difference from 38 to 28. Not sure how much of a difference for a 32 to 28. Other factor to look at is your weight and the contact area of the narrower tire and how the tire get sqeeze and what max PSI the tire can run. I won't go into that because that's a whole different cans of worms open for debate, but you can find plenty of info dealing with that here and elsewhere.

Every Bicycle Tire has them. (Select wire bead for the non pro version.)

I've bought many tires from them, and returned a set with 0 hassles.

28C would easily fit on your rims.

Right. Speed gain not guaranteed. All else being equal, a 28 should be lighter than a 32, but not by much. And, some 32mm tires are lighter than other 28mm tires.

28s will fit, but won't necessarily be any faster.

Read this article about High Performance Wide Clincher Tires for reasons why.

Thanks for the info everybody.

I checked every bike tire earlier today, but only saw the "pro" and didn't know that the wire bead was 'non-pro'.. thanks.

check out nashbar and performance bike. I just bought some 700x32's a week ago from nashbar at a good price.

If they are worn out yes you can use them. There are lots of tires out there. Also check BikeTiresDirect. I'm replacing the dirt tires on my MTB with slicks. I expect to feel that difference on the road. You may experience less of a difference. YMMV

You can get quite a lot of bicycle tires through Amazon. Finding a decent set of 700x32s is no problem on there.