Angry humans can take several 9mm rounds to the abdomen and continue to advance.

Bullets also aren't magical death pellets. A bear has about 20 inches of hair, skin, fat, and muscle to get through before organ damage, assuming you miss a bone.

A bear that hasn't committed to an attack is entirely likely to decide "fight" isn't worth it after the equivalent of getting stabbed in the shoulder by a screwdriver.
If it's already decided that violence is the right way to handle the "you" threat it may continue to attack until it cannot. Then it becomes relevant that many guns don't have the power to disable a beat before it gets to you and does serious damage. The bear dying in 30 seconds doesn't help you if it's last act is to break your arm, and put a two inch deep slash in the side of your neck. The goal isn't to kill the bear, the goal is to keep it from attacking you. That requires a lot more gun, since the near can move and attack very fast.

This is also deep in the realm of "what if". Most bear encounters involving a firearm resolve successfully without even shooting the bear. They don't like loud noises and will run from basically anything. The most encountered bears will usually run from shouting and waving your arms.
But if you're looking to get a gun for bear defense, you need to consider that they're extremely durable critters, and to cover what can happen probably requires more than most handguns can deliver.

Avoidance is a better first defense, followed by pepper spray.