Bloomington Caves Question

Is there anyway to get into the Bloomington caves now since the government is down? We were there a couple of months ago and we wanted to go back to the cave, because it is so big and fun to explore. We did have the combo lock code, but we lost/threw away the paper. Is there anyway we can get in?

Is this area within a National Park? I don't know much about it but I didn't think so.

This cave is not in a NP, but on BLM land. It is managed by the St. George BLM office.