As others have said, knowledge of anatomy is really important. Here is what I learned after killing and butchering a 194 lb bear last year:
1. The ribs are round in cross-section. They are about the diameter of thin pinky finger or thick pencil. In contrast, deer and elk ribs are flat but about the same thickness. Thus, there is more room between ribs on a bear, and the ribs are easier to break/cut.
2. The vitals are more forward than on a deer/elk. Keep your arrow tight behind the shoulder.
3. Bear's shoulders are very movable and not connected to the body by anything but muscle. A hit by an arrow will almost NEVER penetrate because the shoulder structures absorb the energy.
4. When you get the skin and fat off of a bear, you will be amazed at the small size of the bones and muscle structure. This means that the target is significantly smaller than it looks.
5. Bears use a ton of oxygen to fuel their muscles, but they have a lot of lung capacity. This is why they go down so quickly with double lung hits and go so long with single lung hits.
I shot mine with a 125 gr. screw-on snuffer from a 600gr arrow. I got 10" of penetration into the ground on the other side. The bear went 20 yards, and the blood trail was OK, but took 15 yards to start. Next time I'll be using a 160gr snuffer for a larger hole.
Hope this helps!
Brett