If you need to stop a bear, 357 or 44 with magnum rounds is the way to go, as others have suggested. Not sure about 10mm but it's a good round, if you're confident in it I suppose it could be a good choice.
Now, any firearm is effective, as they scare easily. They are grazers, seeking food and conserving energy whenever possible. This is, remember, a large carnivore that survives mostly on berries and insects. They will try fishing along a bank but are not that good at it.. The do not even like to chase game. If after a deer-family animal, they try to follow and take the fawn.
Even when hunting moose, they will only charge for brief distances, jump on the hind, and claw it. It will run away, the bear will follow and try again a few more times over the next day or three, but even then they rely on blood loss to make the animal weak and take it when it's down. Although humans are potential food, they are also wary of humans and see us as "too much work".
Even a .22 will generally do the trick with no blood, a few rounds in the dirt nearby is effective.
A charging bear is not that easy to put down; their heads are thick and on all fours it protect the vitals, it's more or less in the way. Plus once a bear's heart starts pumping in a "flight or fight" state, they can run at you for a surprising distance *after* a fatal shot has penetrated. Although bears are notoriously lazy, if they do decide to expend some energy they do it 100% and are alarmingly fast runners. I have seen large Weatherby rounds from a rifle kill but not stop a bear from running for a half dozen more steps.
I don't like to see bears shot. I think they are majestic animals and more fun to observe than shoot. I know there is a certain group of hunters who seem to see a bear hunt as some he-man adventure, but the reality is you are just shooting a giant sloth, and a guided black bear hunt is the cheapest guided hunt you can buy, so maybe it means you're a cheapskate too. There are also people who go camping hoping to see a bear so they can shoot it. I won't say anything about that, you can guess how I see that.
Other species of animal when hunted are much greater challenges. No Hunting Guide I know is impressed by someone who says "I shot a black bear". The general public might be, but not them or I. A dead black bear to me is a tragedy, not a trophy. If you want to impress someone, go Grizzly hunting.
The claws are razor sharp; I've seen small black bears leave deep scratches in glass windows when they enter cabins searching for food.
But they are not much different from any wild animal; there are plenty with potent weapons available, and black bears rarely charge (they may do a "false charge" but back off after checking if you are a runner or stand up to them). Human-bear encounters that involve contact almost always means a surprised bear rather than one who has room to exit.
A pack of wolves will leave nothing ... I mean nothing ... left of a deer carcass in 20 minutes. Even small animals can cause serious damage to a human, and as far as animal encounter fatalities go, deer kill more humans in America than any other animal (they knock you down with a front kick and then pounce on your prone body ... 60 puncture wounds is not uncommon on the corpse). Even then, it's almost always a surprised deer with no exit who reacts that way.
So it's wise to keep the "cute" factor at bay, and stay calm. You will survive the encounter with perhaps nothing more than a story to tell and no need to call the CO to report your out-of-season kill.
Two more things about camping and bears. They stink to high heaven ... if you're downwind, you WILL smell them before you see them, probably. And they move very slowly and very quietly. I *wish* I could move through bush as quietly as a bear. You probably will not hear them.