How do I find out what contractors are on my base?

Hit up Post HQ. Perhaps they can guide you to the Contract Rep.

You can also go to fedbizopps.gov and search for the contracts on your base. They would list subs under the primes as well.

Go right to the source. If you see a civilian contractor, ask who their company is. They'll probably be more than happy to tell you or maybe give you their card. That's what i did quite a few times when i was preparing for retirement.

Also try Indeed.com or SimplyHired.com (or other job sites). Just type "government contractors at (where ever)" in the search box. That'll give a good indication as well.