I have killed many bears while living in Alaska. They have heavy muscle. The difference between a bear and a deer is you want to break the shoulder of the bear...so he wont run off into thick brush. Tracking a wounded bear in thick brush can become spiritual quickly.
With that being said-they are not bullet proof. Use a heavy for caliber premium bullet and you will be fine. IF I were using a .270 I would look at the Barnes TSX bullet and feel very confident.
Please dont shoot a small one like over at Bass Pro Shop. They have one on dispaly there that is smaller than a black lab..If the ears are small in proportion to the head you are looking at a good bear. If the ears look small, you are looking at a very young bear.