Would it might help to run a sprinkler around the chicken pen? That would be a way to keep the ground nice and wet so it conducts electricity well, to help make the bear's first shock memorable. (I am assuming the bear will come back within a few days, and hopefully touch the fence at that time...
The dogs will probably get shocked once or twice, and then leave the fence alone.
You will need a strong electric shock to deter the bear.
But if there is a way to adjust the level, you could let the dogs have their first shock at a lower level, and then set it to bear-level. (I have no idea...