If you're gonna make a rug, make the ventral cut from neck to tail, then cut straight up the legs being careful that the cuts intersect and meet. The Alaska state bear skinning guide says to go up the middle of the legs, but some taxidermists say it's better to cut straight down the leg from the shoulder to the front of the wrist on the front legs and to go right down the back of the leg on the hind legs. This saves more pelt for the middle of the rug that has to be sewn together and minimizes what they have to trim in the front. If you go from the middle of the heel to the center it leaves excess on the front that has to be trimmed and you lose that area that would be added to the sides if it was left on. I hope I'm making it clear, it's kind of difficult to describe in words. If it hasn't gone into rigor by the time you get to it, lay it on it's stomach with the legs stretched out and make the leg cuts where it meets the ground. Confused? Me too...lol! Don't cut the pads off, the taxidermists like them left on. The Alaska skinning guide says to cut them off, but my guys say no! I guess it's a location thing, but the pads tan up nice and add to the trophy if you leave them on.
As to the quartering, they work up pretty easily. The good cuts are in the hams. Bears don't have back straps like elk and deer. I use Alaska Gamebags, get them for $10 bucks. Bears are thin skinned and they cool out fast unlike elk and deer that hold heat with their thicker hides. It's still a good idea to take care of the meat as quick as you can, but don't worry if you have to leave one overnight. If you get on it early the next morning it'll be just fine. Skin out the legs, cut them off and bag, bone out the back and flanks, take the heart and liver (be careful, bears have gall bladders) and you're done except for the packing. Joint the paws at the heel and leave the pads entire. Skin and bone the skull until you reach the Atlas bone (First cervical vertebra) it's an easy matter to joint it with a knife. Cut through the sinew and cartilage and give it a sharp twist. Fold the hide against itself hair out. Lay the head and paws on it and roll it up and bag.
Bear meat is great meat. It makes everything from pot roasts to pepperoni. Great burger, sausage. Take it a processor that's done a lot of bears. I like Custom Meats in Eugene. They do a great job.
If you're going to do a mount, you should make a dorsal cut and case skin the legs. Good luck!
http://www.theidahosportsman.com/bear%20anatomy.pdfWish I could take credit for that! That was a reply I got to the same question.
Good luck, we're still snowed in here, at least our hunting spots are.
Lucky