I live on a military base do I still have to go see the sheriff?
Now thats a good question. BTW, you don't have to go see them, just send them a copy of the application. It's just sort of an FYI to them, so they can write to the BATF if they have any reason to object.
I would speculate, that since neither has jurisdiction on base, you might send to the head of base security. All sort of depends on how long of a tour you have left. Since any purchases have to be sent to the address on the license, you might be submitting a lot of address change forms. Hard question to really answer.