I have shot a lot of deer and I would think a bear is as tough as a deer as far as being able to keep going after being shot.  I’m a good shot and have put a 12 Gauge slug through the heart of several deer.  It is common for a deer to run 100 yards after having a slug put through their heart.  My point is I do not think a bear will just die instantly after being shot. If you do hit him in the heart he is going to be mad and excited for several minutes.  Spine shots generally stop an animal and drop them in their tracks. Place your shots carefully gentleman.