The idea, when hiking alone in bear country, is to bring along a friend. That way, when the bear shows up, you’ll have someone you can hopefully outrun. You’ll never outrun the bear!
My friend would be in a caliber larger than .44 and the extra weight would add to your workout. Why people go unarmed in bear country is beyond me.
That's why a small dog is as good as a large dog. Either one will warn you about the bear, either one will bark and antagonize the bear for a moment or two-long enough for you to start running, and either one will take long enough for the bear to eat for you to get away.