What English term do you use in this context?
"When you are getting to the other side of your room, but you got no choice to walk / step on your bed."?
Well, climbing does work in this context, but there is another way to tell. Tiny rooms with large beds are nothing but discomfort to the tourists and that's why, you see a lot of complaints made by the visitors visiting hotels worldwide.
Two such examples I came across on TripAdvisor where the visitors had to walk over the bed to go to the other side of the room. In fact, one of them posted a photo of it where the arrangement of other furniture is such that it's difficult to pass by the bed. The exact case that you described here.
I would climb over the bed.
I had to climb over the bed to get to the window. (Because there is no room to walk around the bed.)
An idiomatic usage as far as I know, but see climb:
- to move (down, over, along, etc.), using the hands and feet