The best way to prove a base exists in Dulce is to track down the logistics needed to support such a base. The only thing the episode showed us was that such a base is possible. The government has built many secret facilities for our leaders if a catastrophe happens. The problem with that part of the show is that such facilities have a skeleton crew at best. A place such as Dulce would be manned, and the personnel there would need to be supported.
The Native population seem to look at visitors with amusement. I did think the Native who guided the crew of UFO Hunters seemed to be yanking their chain. I think one has to look at the possibility the locals want the Dulce area to become the next Roswell and attract visitors willing to spend money there.
The best thing to do would be to get a few people together and look for traces of support. If there is an underground railroad or mag lev system, it would need a large support system. Someone needs to inspect and repair on a daily basis. No matter how perfect they are made, the earth is always moving and causing cracks. Leaks in tunnels are quite common, and a maintenance crew would be needed to fix them.
Is there a railroad spur that goes near the area? What about roads? Are there runways for large cargo planes to bring needed supplies? Also, they should look for workers, both present and former to tell their stories.
Before one can tackle what goes on at a certain base, one has to prove the base exists.