Not sure if it is open on a regular basis (when I passed by on my last few trips, the gates were always closed), but if you contact them you can probably get in. Joseph's Cave is now affiliated with the Alvynegril Guest House across the street (same owners) and the cave is open to guests who stay there. Maybe if you contact them ahead of time (try the website below), they will let you in to the cave and have the bar ready.

http://alvynegril.com/