I'm going to put riser bars on my road bike. It's a Felt and has 25 gears.I'm going to put Shimano 3x8 speed shifter/brake lever combo because the Simano 3x9 cost double the price on the 3x8 on Ebay is like $25.That would put me at 24 gears which is just fine.I don't need 25 gears.With that shifter missing one gear.Will it work? or will I just not have access to that last gear?

An 8 speed shifter will not work if you have a 9 speed cassette.

Your bike does not have 25 gears.
You don't have 24 or 27 gears either.
You can have 24 or 27 different combinations.
Some of those shouldn't be used due to cross-chaining.
Some are repeat ratios.
As a crude rule-of-thumb, expect to have about 2/3 as many usefully different ratios as you have possible combinations.

Opinions on mixing 8-/9-speed vary.
8- and 9-speed cassettes are equally wide.
So the sprockets are spaced tighter by some fraction of a mm on the 9-speed.

Now, (at least) Shimano derailer pulleys have some sideways float.
Which forgives a bit of mismatch.
Even mixing 7/8-speed will usually kinda-sorta work.
And they have a bigger difference in spacing.
Whether or not you'll be content with the performance is impossible to say.
Degree of wear, tune, shifting style and rider expectations tend to play a big role in how satisfied someone is with a mixed drivetrain.

I don't think that you have that quite right. 7 and 8-speed cassette cog spacing are the ones within a fraction of a mm with one another. 8 and 9-speed varies by quite a bit and won't mix/match. Assuming OP has a 3 x 9 drivetrain now, if he wants to use an 8-speed shifter to save money, he'll need to buy an 8-speed cassette so I doubt he's going to save anything. I'd get the 9-speed shifter.

25 gears isn't possible. It has to be a multiple of 2 or 3 front chainrings x the number of rear cogs.

In general, compatibility depends on three things. Any of these can prevent the shifting from working correctly.

The spacing between rear cogs.
The cable pull distance per click from the shifter.
The amount of movement of the rear derailleur when the cable is shifted.

There are some workarounds to get non-compatible components to function. A few incorrect combinations will "kind-of" work, not quite lined up, but close enough for some riders.

So,
post your rear derailleur model, and the number of rear cogs you have.
You can post photos by clicking "Advanced" and use the paperclip icon to upload a photo.
You'll get more useful answers.

Shimano 7-speed is 5 mm spacing.
Shimano 8-speed is 4.80 mm.
Shimano 9-speed is 4.35 mm
So yeah, roughly twice the error mixing 8/9 as mixing 7/8.
Never said I thought it was a good idea.
But I've ridden with people claiming to be happy with it.
I might try it, If those were the parts I had home.
But I wouldn't buy mismatched parts like that.

" Gear" = a ratio .... count teeth, use those numbers.. a 40 tooth front sprocket turns a 20t hub cog twice.
We call that a 2:1 ratio.

Popular is to then multiply the ratio by the wheel diameter, measured in inches.. that is called 'gear-inches'

There are a lot of things you do not understand about your bike. It is mathematically impossible for it to have 25 gear combinations. Next, an 8 speed rear shifter wil not have more than about 4 gears working if you have a 9 speed cassette, the 5 others will be very noisy if they engage at all. If you have a road bike you have to make sure that the brake levers you buy will work properly with your calliper brakes, mountain bike levers are mostly made for v-brakes and will not give you enough leverage. If you buy 3x8 shifters,make sure they are made for road derailleurs, mountain bike shifters will not work with your front derailleur, they pull the wrong amount of cable. So, buy those cheap shifters as long as you don't mind front and rear shifting that doesn't work properly. After all, they are cheap and nothing else matters

Assuming this is for the Felt F70 you list in your profile, and it has original equipment, you have a 3x9 shimano 105 drivetrain. The all-in-one shifter you're referring to are more than likely mtb shifters. Better choice would be going with the Shimano Sora 3x9 flatbar shifters that are designed to work with road bike drive trains like yours. About $50 on fleabay. You'd need a separate flat bar brake lever.