Fish & Game won't do anything till there is a attack or someone gets hurt.
hopefully the ruckus your dog will make will be enough to keep them away. Yes black bears are skittish but the last statistic I saw showed more people up here are killed by black bears than Griz because they assume a black will run! A Griz you either kill or steer clear of because you assume he wants a fight.
As a possible deterrent, get a few cans of Off bug dope or similar that are pressurized and cake them with bacon grease. Set them where a bear will get them but not your dog or most other predators. (in a wire cage nailed on a tree?) If a bear comes thru, it will go for it, he will bite the can and when the can blows, it will decide the taste in his mouth is more important than your birds. Now you have run off the bear and have proof for Fish & Game that it's a problem.