I doubt that any self respecting bear would come anywhere near a chainsaw anymore then they would run into a forest fire.
Unlless you were trying to ride one her cubs bareback, a chainsaw running full bore would simpling be too intimidating. Not because of it's cutting ability, but due to the high decibels.
I worked in Toba Inlet on the West Coast where Grizzlies were thicker then thieves and some of the loggers would not even shut their saw off they were so sh!t scared.
Ive had many encounters with bears wolves and even a cougar once, but never was charged, except once in a boat on a lake close to shore, but I think it was just a glorified bluff. Bears are opportunists and will rarely risk a confrontation unless provocated by iterference with young or a recent kill.
It's hard not to be scared, but bluff them out whenever possible. Using excessive force such as a gun is seldom required.
John