Where's the second cave?

I think you're thinking about the moaning caverns

There is only one cave, but there are two entrances that are connected (can enter through one and exit by the other, but only swimming!)

1 is down stair the 2 cave is on opposite side..less than 2 miles.....

Natural Bridges to my knowledge doesn't have a second cave. I floated through the main cave and you come to the other side of the bridge. Hope that helped.

There's a cave a few minutes up the road you can pay money to tour called moaning caverns. The entrance to the cave has a gift shop built over it where you can buy gyms and snacks. Moaning caverns is large enough to fit the statue of liberty inside of it. It's worth the tour. Long ago they used to let you pay more to repel down to the bottom of the cave via rope/harness. But I didn't see that offered when I went there this summer.

A waterfall flows over the cave entrance, moving further into the cave it narrows, where people take rafts, inner tubes