When we have been lucky enough to bring a bull back to camp, we will clean it up like this.
First thing we do is get a HD black industrial trash bag and wrap the skull in this very tight and tie it up good. Then we take an air nozzle, the one in the shape of a pistol with a 6-8" needle for blowing air into tight spaces. Cram that down through the back of the skull and make sure you got a full tank of air, turn your head and squeeze quickly a couple times. First blast tends to blow the whole brain right out another hole, thus the heavy duty trash bag. Once that is done, I move to stage two.
I had a guy in a welding shop build me a oval pot with a skirt around the base. It's deep enough to drop the whole skull in, but not wide enough to allow the antlers to get into the water. The skirt goes over the turkey fryer base and keeps more heat in under the pot. I take a 20 pound propane tank anyways for the little Webber grill, so I have plenty of propane to boil out several skulls.
I add some Borax to the mix and monitor the water level from time to time and basically cook all the rest of the meat off until the skull is fairly clean. Then I pull it out and let it cool just a little, and take a fillet knife and scrape off all the loose pieces. When I'm done with this, the skull is very clean with no brains inside or flesh outside.
For the hide, we generally will clean as much flesh as we can off, then fold it up and put it into a trash bag and drop it in the deep freezer in the back of the camper. We have salted the hides before, but I have found most taxidermists don't like them salted but prefer them frozen.