In my old apt Samson was in a spare bedroom. He learned how to jump straight up out of his cage and onto the nearby bed- He didnt chew anything but PEEEEEEED tons and tons all over a left lots of poos claiming it as HIS. I tried everything to block access out of the cage (sheet tied ontop- he would pull on the cage until there was a small area he could get out through). Eventually I found out that a shower curtain laid over the bed worked the best. Maybe this will work for you?

Shower Curtain!!! Plus they are a cheap fix Get the slippery kind

You could try putting a fence around the bed, a foot or two away from the bed. That makes the jump wide as well as high and he may not try it any more. I haven’t done this, so I can’t tell you how well it works, but I would think that it would, as long as the fence/barrier is high enough to keep the bun from just jumping over into the “no man’s land” between the bed and fence and from there to the bed. I’ve found that Leroy won’t jump over a fence made out of NIC cubes (if you don’t know what those are, search this forum, there are a bunch of threads about building houses/fences from NIC cubes) that’s only 1 cube tall (about a foot high) but he’ll jump only my bed that’s a good 3 feet off of the floor because he knows/can see there is something to land on.

The only reason why I suggested this rather than the shower curtain was becasue personally, I would think stepping over a low (for us) fence to get to bed would be easier than dealing with a tarp or shower curtain every night before climbing into bed. Though if you have young children who frequently get out of ben in the night for the bathroom or because of nightmares, the last thing you want is for them to trip over the fence in the dark!!!