Why does your bunny move his bedding around and scratch the bottom of his cage?

Moving around his bedding, and scratching at the bottom of his cage, are normal bunny play behaviours.

In the wild, animals have to work to stay alive; when they're domesticated (pets), animals don't have to work because we provide everything they need, but the same work behaviours are ingrained in them and they need to be able to express them by playing. Digging in the dirt and pushing it around is a natural behaviour that wild rabbits do when they build their tunnels, so many pet rabbit like to do these things in their cages.

To help your rabbit be a happy, fulfilled rabbit, you should provide toys and play structures that he can use to vent his natural behaviours on. See the related question below for more information about rabbits playing and good toys.