Flesh the hide thoroughly, including turning the lips inside out and the ears as well.
Remove all the flesh,fat and especially blood that you can, and then rub plenty of salt into the hide. Really rub it in! You won't hurt it. Make sure you get plenty around the bullet holes and anywhere there is blood. It will take at least five pounds of salt for an average black bear.
Fold the flesh side of the hide together, roll it up and put it in a shady spot to cure. Open it up after 5-6 hours and you will see how the moisture is being drawn out of the hide.
Salt again in any places where the salt has been completely dissolved or it appears there may not be enough. Again, be sure to rub it into the hide well. The hide must be completely covered. Fold and roll it up again.
Do this several times and you will notice that the hide is shrinking and getting "tough" as the moisture is drawn out. Usually by the next day, after having cured overnight, it will be ready to dry.
Open it up and rub the remaining salt around on the hide and then carefully hang it over a branch or pole to dry. IT MUST BE IN THE SHADE TO DRY, NOT IN DIRECT SUNLIGHT.
Keep checking as it dries, and when it starts to get quite stiff roll it up and allow it to finish drying. It will keep for years like this, and your taxidermist will be very pleased with you.
If you wait too long to roll it up after curing, it will become too hard to roll and will be like a piece of plywood. Won't spoil, but will be hard to handle.
If you are not going to have it tanned, then hang it up by the nose for the final drying. Just hook it over a branch high enough to keep the legs off the ground. It will dry in this shape, and you can then hang it in your den, shop or wherever you like.
Ted