If it's already been picked over by the bugs, then the first step is degreasing. Big bucket outside with the hottest tap water you've got and a ton of Dawn detergent. Squirt the Dawn all over the skull, in the crevices, in the brain cavity, etc. and add a bunch to the water. Soak the entire thing (make sure the water covers the antlers, or you'll have a line across them where the water was) for 24 hours or so. Dump the water, hose off and repeat the Dawn soaking. Keep doing this until you think it's really clean. Feel free to use a toothbrush here and there, but nothing stronger than that. Set it in the sun to dry. If you see any dark patches on the skull, you're not done degreasing, so try some more.

Bleaching: go to Sally Beauty Supply and get some 40 Volume peroxide and activator powder. Mix together to form a paste, and brush on everything you want bleached. Allow it to dry completely overnight. Next morning, hose it off and set it in the sun. Repeat the process until you're happy with the outcome. Once you're happy, let it dry thoroughly, and spray it with a sealer.

Or, your taxidermist would probably be happy to do this for you for a small fee