I rode “shotgun” for Castle Mountain Outfitters in Chickaloon AK on their trail rides back in the 90s. I carried a rifle - not to shoot any bear but to hopefully scare them off. We made enough noise that in the 4 years I did that (week-end volunteer during the summers) we never had a close encounter.
You want to run them off before they claim territory.
Ive only been around black bears.
I have been in Griz country at Glacier park in Montana, but did not encounter them, and I am kinda glad.