What kind of bedding are you using? I never bother putting bedding in their hidey areas, the entire cage has a layer of newspaper and then half of it has a layer of hay then the hidey area is placed on top they sometimes drag some hay along with them but they feel secure enough in the hidey places as is without adding extra bedding.
If they are outdoors they need their sleeping are to be full enough with hay so they can bury themselves in it.
I guess if using something like Megazorb it depends on the size of the housing and how often they are cleaned out but an inch to inch to two inches should be enough. With newspaper underneath to make cleaning easier, just roll it up and chuck it.