Get your pen and paper ready - this is the easiest method that doesn't use beatles.
Get a bucket, fish tank heater (about $10), fish tank thermometer (floating kind, about $3) and one fresh road apple (horse turd - sometimes it comes out of a Democrats mouth too).
Fill the bucket with hot water, set the tank heater in it and set it for 100 degrees. Drop the road apple and your skull in (clean off as much meat as you can). Drain off about half the water each day and fill with hot water.
Your skull should be clean and ready to bleach in about 3 days. I did a cougar skull this way, and the bacteria in the turd eats EVERYTHING - the brain, eyes, etc. will be completely consumed and you won't have to do any digging.
Be careful when emptying the water each day - it STINKS! Also, at the end, you will need to be careful when rinsing out the bucket to avoid losing any of the teeth that fall out.
This technique was taught to me by a guy that worked at the Smithsonian, and they used it for very delicate skeletons.
One last thing - the temp is critical. If it is too low the bacteria won't be vigorous and nothing will happen, and if you go too high they will die.