I know this is an old thread, but...
Live in the Ozark National Forest. Specifically where the game office drop off bears that are written off as "trouble makes" caught near residences.
Last March I was charged by a rather large, male, black bear...the only thing that saved my bacon was a dog named Doo. Not "Scooby-Doo", but "Doo". Then there are the dozen or so encounters where the bears came into my yard that Doo ran up a tree. Then there was the time a bear busted out two of my windows. Bears here are not afraid of people.
Long story short...a dog is a must. If you walk in brown/griz country...I'd take at least three. Don't have to be big dogs. Funny thing is...black bears can count. They tend to think twice with one dog, but two dogs....they will take cover rather than advance. Three dogs...no worries.
Half guard dog and half hound is a good bet. Best of both worlds without them straying too much. With that said you don't want the "half-hound" to be red-bone, blue-tick or anyother hound adept at running 20 miles a day. You will loose them in short order. A mild hound like a "water-dog" (lab/weimeraner) mixed in with a BIG guard dog (mastiff/dane).
Any LARGE pure bred guard dog will do, but they cost money while muts are typically free. Even a single teacup poodle is better than nothing...assuming you can out run the dog of course. A single pitbull will work, but you can't run more than one cause they'll fight your other dogs if not kill them.
With my experience with black bear...I'd never test my luck with brown/griz...