It entirely depends on the bear species, but in general guns are a last resort defense against bears.

Primary defense is avoidance and making it so they can avoid you. A bear will eat you, but is unlikely to hunt you. For most bears we're an unknown quantity so they'll avoid us, since other food is reasonably available with less risk.

A bear has heavy fur, thick skin for storing winter fat deposits, and dense bones. While bullets will injure the bear and perhaps even kill it, it won't be enough to save you.
Much like how hitting someone on the head with a glass bottle will hurt them, almost certainly injure them, and potentially kill them, the type of injury is likely to be a fractured skull or brain bleed. Extremely serious and deadly, but they have minutes of functionality and hours of bewildered stumbling before they black out.

So it'll likely die... Later. For now you have a scared, confused and pissed off bear.

I believe hollow points have less penetration power, so it might not even get through the hide. Other bullets will get through fine, but are unlikely to stop the bear dead.