The bear seemed to... nod at you before it looked towards the inside of the stronghold. Seems like there'd be something in there to help you and the bear out. In fact, you can clearly see a wagon of cabbages inside the entrance to the stronghold. It could help provide a way out as a ramp of some kind.

Of course, it would also catch fire if it came into contact with the fiery barriers. You'd have to find another way to use it.