Numerous black bears have been killed with the 38 Spl but it is not a very reliable stopper. I personally know of 4 bears that have been killed with a 38 Spl by LEOs and a dozen or so by houndsmen. In the first, that is all the officer had and in the latter the bears were treed and the shot can be placed very precisely. If one had no other choice but a .38, the best bullets would be solid (not hollow point) semi-wadcutters or round nosed bullets. These may give you the penetration needed to reach the vitals of the bear, hollow points will open up much too fast and may not even penetrate the hide and fat on a bear in the fall. If it is at all possible use a bigger gun as even a .357 is pretty marginal under the very best of conditions with the best of bullets.
In reality, unless you intentionally go looking to tick a black bear off, a loud shout and making yourself appear bigger by raising your arms out will send it scurrying. Few people see black bears in the wild, especially under 100 yards, as black bears are fairly wary of man and do generally their best to avoid us. I've lived in bear country most of my life and the number of times I've walked up to one while out and about can be counted on both hands with several fingers left over. It takes an awful lot of luck (good or bad depending on the individual) to get close to a bear in the wild and is not something I worry about, definitely less than stumbling across a temporary meth lab.