I agree with all of the above
Bunnies don't need "bedding" the way hamsters or mice do...but I do use fleece baby blankets (receiving blankets work well) and layers of flannel sheets on the floor of their bunny room. (Mine are not in cages...they free-range with a separate bedroom as their headquarters).
In the bunny room, they have a table covered with a flannel sheet that comes to the floor on all sides as their "private" bed place...I put baby blankets in there and they arrange them very specifically in pillow mounds and valleys and they love snuggling up, stretching out and sleeping in there.
They make little "doors" in the sheet cover for exits and entrances (by pushing the sheet up with their noses not by chewing) and they peep out to see what I'm doing. They think I don't know where they are
After I wash the baby blankets, the bunnies spend a long time in there "fixing" them the way they want them. Both bunnies are litter box trained and they never pee anywhere else. There might be a poop or two in the "private" room but they keep it amazingly clean.
They seem to feel really safe in there. It's where they run if they hear a strange noise or if I bring a new person in to meet them. I try to go under there only to clean so they feel like it's really a "bunnies only" private haven.
:brownbunny:heartbeat::brownbunny