Left: When presented with a quartering away shot, aim to place the bullet in line with the offside shoulder in order to penetrate both lungs and, with luck, break that shoulder and put the bear down right there.
Center: Though it's been written that an immobilizing shot to the shoulder is best, every experienced bear guide I've hunted with recommended a lung shot. Place a bullet tight behind the shoulder, and your bear won't go far.
Right: This shot angle presents the best chance to break down a bear on the spot. Drive your bullet through the near shoulder and both lungs. You'd better have a tough bullet with high sectional density to aid penetration.
It has been written that a shot to the shoulder is best for shooting a bear, since it immobilizes the animal. Down through the years, I have hunted black bears and grizzlies with a number of highly experienced bear guides, and all disagreed with that line of thinking. Each and every one recommended placing a bullet close behind the shoulder and about a third of the way up the body for maximum damage to the lungs when the animal is standing broadside to the gun.
I have taken most of my bears with shots to the lungs and don't recall a single one that ran over 100 yards after being struck; most bit the dust inside 50 yards. A Boone and Crockett interior grizzly I recently took with the 7mm STW was a good example. Standing 319 yards away when I fired, the animal fell dead no more than 25 yards from where it took a single 160-grain Trophy Bonded Tip bullet.
A shot through the shoulders is sometimes recommended should it become necessary to finish off a wounded bear. It may also be the best bet when shooting a grizzly inside 50 paces, but you had better know your bear anatomy and you had better be using a tough bullet of high sectional density when doing so. Otherwise, I am convinced the first shot should be through the lungs.
Moving from a side-on shot to an angling shot complicates the issue. If the animal stands quartering away, I aim to place the bullet in line with the offside shoulder to penetrate both lungs. If it is quartering toward me, I aim for the near shoulder and drive the bullet back through the lungs. I really don't care for the full frontal shot because the bullet can pass between the lungs without doing a great deal of damage to either of them. But sometimes it is the only shot you get, and placing the bullet in the center of the chest just below its juncture with the neck is the best bet. Just make sure your aim is low enough on the chest for the bullet to pass beneath the lower jaw rather than into it.
A lot of black bears are taken from elevated blinds or stands, especially when hunting over bait. The closer a broadside bear is to the gun, the tougher the shot becomes simply because as the angle increases, target area presented to the shooter decreases. If the animal is hanging out beneath your tree stand, it is usually best to reduce the angle by waiting until it moves farther away before shooting, but if you must take a close-in shot, visualize the location of the lungs as you very carefully place your bullet. If it is standing facing directly to or away, a bullet down through the center of its back just behind its shoulders will break the spine for an instant stop.
One last tip: Hunt bears long enough and you will enjoy one-shot kills on some, while others will require follow-up shots for reasons ranging from obvious to unexplainable. When shooting any potentially dangerous animal, keep pouring in the lead until it stops moving. Shooting the very last wiggle out is how I describe it.