The Bebop seems to use cylindrical force to create artificial gravity. (spinning a cylinder inside itself to create a pull against the walls similar to gravity) If I had to guess, that's what a rounded off part on the back of the Bebop is. Just housing for a cylinder. It seems to be where most of the crew spends their time. The Bebop is a sizable ship, so I suppose that makes sense, but if that's the case what is in the front part that looks like the stern of a boat? Is it all storage? How is there gravity on the main deck at the top? We see Spike and Jet there a couple of times and they aren't floating at all. Just standing as if there's gravity. The famous "I heard a story once" scene comes from that room.