I just got done doing exactly this. I am a 3D (communications) but wanted to get my EMT-B. I had done a lot of prep work prior:
- Volunteered hundreds of hours at my local military ER
- Read the whole EMT-B book prior to attending the class
- Sought permission months in advance so there would have to be a really good excuse to make me drop the course.
I went through Central Texas College Europe, which had a program that ran in the evenings. I still had to leave work early because I am a shift worker and work Panama's but thankfully I had a great instructor who understood this. I also had to take a day of leave for one of the weekend all day classes, but 1 day of leave isn't anything.
Our hospital used to offer the classes on base to whomever was interested. I was one of the instructors. It's not that big of a deal. It's just a glorified first aid course. If you scored well enough on your ASVAB to get into the Air Force, you should have no problem with it.
We worked 24 hrs on/off and had a Kelly day off every other week. Got K day moved to Tuesdays, took night classes at local community college. Then I worked ambulance my days off, and my EMT-A certificate let me skip the second half of rescue school and got me onto the rescue truck permanently.