Ruby is a 3 year old English spot, she lives in our bedroom. I don't have video but I did find a couple of videos online, they show a little of the behavior. I have talked to others who's bunnies have the same habit, so it seems pretty common. It is hard to get good video because once I get the camera out she gets distracted.
It will often happen just as I climb into bed, which makes wrinkles. She jumps up on the bed, gives me kiss, then starts pushing the wrinkles out of the bed. Her hind feet placed firmly and she pushes out with her front feet. She moves forward and pushes some more. After a couple of minutes she stops and snuggles in for bed time petting and snuggles.
The other time it happens is shortly after my wife makes the bed. Ruby will jump up on the bed and make sure all the wrinkles are pushed out. She will occasionally dig a bit like you see in the videos, but it is 90% pushing. Some times she pushes so far ahead that her back feet slip out behind her and she is stretched out in superman position (arms straight ahead, feet straight back, and on her belly).
I can understand the digging behavior, but what is it that causes a rabbit to push wrinkles out of the bed?