I have done a lot of solo back packing in bear country. Black Bears are emotionally unstable. One day they'll be nearly tame and the next, they will try to "take you". I have been on the autopsies of a rather large number of black bears. They are heavily muscled and have large bones for their size. Personally, I would be more happier with a revolver caliber that starts with .4 (.41, .44, .45). However, a .357 magnum will do the job with a cool hand at the handle. A .357 magnum gains its power from velocity. Using a short barreled .357 is giving away the "magnum" in it's name. I would not consider under a four inch gun. I would load a heavy for the caliber (180 gr) cast bullet with a wide meplat and a full load, at that.

Black bears are not to be trifled with. Normally, they'll leave an adult alone but I sure would not let a child alone in the yard in bear country. That is just asking for it.

Think of it this way - would you leave your child alone in the yard with a 300 lb junk yard dog? Of course not - well a bear has a about three times the strength of a dog and is better armed. So, just take proper precautions.

The dirty little secret of several of our National Parks are the maulings from black bears. They get little publicity as the powers that be don't want to run tourists away. A good number of the maulings occur from idiotic moves by people but some of them are unprovoked.

FWIW
Dale53