How about not using bedding for the bunny. Use 1/2 inch hardware cloth on the floor of the cage with no tray so the urine and poop passes through the mesh and falls on the lawn. Move the cage around frequently so it doesnt pile up in one spot and almost never have to clean up at all. Everything will be spread out and compost naturally.
If you do it any other way you may decide you don't want bunnies because the odor of their urine will knock you out and they poop constantly. You will be cleaning all day and all night long.
I had a pair of bunnies inside and used both pine shavings and shredded newspaper. Either way they sprayed urine across the room on my walls, in my curtains on the floor. The whole room stunk and I was cleaning twice a day. When I moved them outside to a pen with a sand floor, things were much better. That is another option.