Mauser,
Like Bareback said, for a rug cut up the belly neck to tail. In the front cut from just behind the feet and out to the center of the chest.
In the back cut from just behind the feet up the leg to just just under the tail.

Use a saw to cut off the feet and head, leave them in the hide.
Keep the hide cool, get it off the bear asap.
Put extra ice around the head, keep it cold.
Get it to the taxidermist with in two days, one is better.
Take the whole hide, this will give you options if you change your mind on the mount you want.

Contact your taxidermist. Often they will have an instruction card you can take to the field with you. Or you can print it off from the internet.

Know your regulation for your state. Some states require proof of sex attached to the animal. Some states require you keep the meat from bears, some don' t.

If you are keeping the meat there are several options. You could pack the bear out whole, you would need to gut the bear.
You could quarter the bear and remove all possible extra meat.
You could bone out the bear, basically cutting the meat off the bones, this is the easiest and lightest way if you are packing it plus the cape.

Good luck on your hunt.