I haven't had any personal experience, but I was told by a ranger near my home (southern arizona) that dogs and bears don't mix.
An area south of town that had a lot of bear sightings last summer required dogs to be on leash and had explicit warnings about dogs. They put a bear down there a couple of weeks ago. It was in a campground and didn't respond when shot with beanbags, so Game & Fish killed it.
A few years ago there were a bunch of human-bear encounters north of town, and a woman's dog tangled with a bear while she was out hiking. According to the newspaper story as I remember it, she at first thought that another dog had attacked hers. She got into the fray to try to break up the dog fight. I think her dog was okay. I remember her picture in the paper; she was covered with scratches and had a helluva shiner.
Later in that same summer in the same area, a girl on a summer camping trip was badly mauled by a black bear. I think AZ Game & Fish paid $$$$ to her after a lawsuit because there had been many bear & human encounters prior to the mauling. The girl who was mauled did not have any food in her tent and had not violated any camping-in-bear-country rules according to reports. Someone shot the bear to get it off of her. Later it was determined that a resident in the area had been feeding the bears regularly -- a woman who cried that the bears needed ice cream she provided. Details are fuzzy in my memory, but I think they could only convict her of disturbing the peace and give her a small fine because there were no laws on the books to address the case. Public awareness material published at the time suggested that bears are easily irked by dogs.
These situations are sad both for the bears and the humans.