First, congrats on your success!!
I have done many European skull mounts and while I still enjoy a shoulder mount, I really like to skull mount those nice deer that do not warrant $400 in taxidermy work.
First, DO NOT use bleach. It is too hard on the bone and will yellow over time.
What I like to do is skin the head asap as it is easier to do before the hide gets taught. Then you can freeze the head if you like and thaw it later for completion.
When you get ready to finish the job, boil some water outside in a large pot and then reduce heat and "simmer" the meat off the head. I usually take it out a couple of times and whittle the meat off to help it clean faster. A taxidermy product called sal-soda can be added to the water and helps with the process.
Just keep cleaning away at it. You have to use a water nozzle to blast the cooked brains out. I use needle nose pliers, etc to gently clean the nasals, etc. If you don't get every bit of meat and other tissue removed, it will smell very bad. I usually let my finished skulls stay in my shop for a couple of weeks before they come into the house.
Once the skull is clean and ready to whiten, I like the whitening powder you can get on line from taxidermy suppliers. Enough to do several skulls usually runs me about $30. You can also submerge the skull in peroxide and set it in the sun, but be careful not to get the antler bases in peroxide or it will whiten them also.
Its basically a slow tedious process, so have some time and maybe a couple of "cold ones" in the fridge on Saturday. That's why I like to do it in the spring rather than during hunting season. If I have more than one to do, I would rather do this all at once.
Good Luck
Smoky