I have soaked in a very mild solution of bleach water only overnight but if you use a strong amount of bleach it will begin to eat at the bone and damage the skull, when it drys the bone will begin to flake off, I found out through trial and error. This one of the skull mounts I have done
I prefer to paint my skull white with a acrylic paint and then seal them with a clear semi glosspolyurethane finsh this will seal the skull from absorbing and airborne smoke ,dirt or air borne grease etc, and makes for easy cleaning, you can just dust and wipe clean.