kmb,
Black bears that become habituated over time can be troublesome, but they usually wont attack humans unless they are provoked.
As far as caliber, your 357 should be fine, but more importantly, can you shoot it accurately under pressure? 4" should be fine. A 2.5 inch barrel is going to lose a bit of velocity over a 4 inch.
Bear Spray would work too, especially if the bear is just being curious. Bears are very intelligent animals and they learn from experience. Just empty a can in it's face and it will remember the unpleasant experience and not come back.
If the bear did any damage to your property, I'd call your local game dept and see if they have any other recent reports in the area.

As for a gun, I'd answer a few questions if you plan on carrying for bear.
1. Is the bear just looking around for trash cans/food or are the ears pinned back in an aggressive manner?
2. If you shoot the bear and its not doing anything else other than poking around, could you be arrested and lose your permit?
3. What if you shoot the bear, only wound it, and it turns on you or your family.

Better to be safe than sorry.