YOu dont need that sort of 'bedding' no. When I had an indoor cage for Muppet, I had wood shaving and a litter tray. I learned very quickly that wood shavings end up EVERYWHERE, even rooms he didnt go in! I quickly swopped to litter tray at one end of the cage and profleece in the rest (similar to vetbed).
I dont have a cage anymore, my two free range completely in the dining room. They have profleece to lie on. Sooty lives on hers. Muppet quite likes to sleep on the door mat in front of the draughty door :roll:
The only 'litter' is in their litter tray. If you have a litter tray outside the cage putting a small doormat down cuts down on the amount of litter tracked through the house, as more drops off their paws there as they jump out. (I also found it useful when the litter tray was inside the cage.)