Actually, FBI prehire physicals are rarely performed at a mlitary base. Generally, a local contractor is used. Most often it will be some type of local clinic that does the same for local PD's, companies, workman's comp cases, etc. A "work & wellness" clinic of some sort. Often, several government agencies will contract with the same clinic and they do physicals for several of them. Once you are onboard, you receive continuing physicals, but not every year, at least until you reach a certain age.
Excercise induced asthma could prevent you from being hired by the Bureau. It depends on the severity and the doctor's opinion. You absolutely WILL need documentation from your current Doc on your asthma and limitations. What you have to keep in mind is that the 2-mile run is simply a minimal that is used for the PT test. Even then, it is performed at the end of all of the other PT test events, so you will already be winded. At Quantico, you will participate in runs that range from 2 miles to 8 miles or more. You should expect run at least one 6k as a minimum. Additionally, on many of the runs you will stop every so often and do various exercises such as push-ups (regular, knuckle, fingertip, front leaning rest, etc), sit-ups, leg lifts, etc. PT is NEVER JUST a couple of miles on the track.
I'm not trying to discourage you. You should realize, however, that it will be an issue you have to face. Get as much documentation as you can and train and medicate (under a doctor's care, of course) to get the most out of your aerobic exercise periods. The upside is that you should know pretty early in the process if it is going to DQ you.
Gonzo