Shooting the bears doesn't seem very permaculturey to me. Traditional farming is an endless battle to kill off "competing" nature. If bears live in the area, there will always be more. So you have to work with what the situation is. There's heaps of bears where I live, people around here manage to deal with it. There's both grizzlies and black bears.
My friends have 9 apples trees and have very good luck protecting them with a simple string of electric fencing. They also have a little bulldog who likes to bark at animals--but the dog isn't always at home. I have two other sets of friends with small farms with chickens and pigs, they they use livestock guardian dogs who stay on the property.