Black bears exist in forty out of the fifty US states, approximately 900 thousand total in this country. For the most part, they are peaceful and wish to avoid people. However, it requires continual feeding to support such a heavy body, and bears are tempted by a discovery of any food source. In other words, food trumps good sense.
If a bear succeeds in tapping into this new food source, it will then get fixated on it. So your objective is to make this food source unpleasant for the bear and to prevent the bear from tapping into it. If a bear succeeds in obtaining food from a source, it will then keep coming back for more, requiring the addition of more pain to interrupt the fixation. I use special non-lethal loads, either hard plastic shotgun rounds or more painful bean bag rounds. This almost always discourages the bear from returning.
By the way, the discussion of non-lethal shotgun rounds always invites comments to the effect, "I wouldn't waste my time with non-lethal rounds, I'd kill the @#$%^&*. " Since I'm not responding here to such a person's comment, I am free to say, that's just stupid and ignorant. Trying to kill a bear is very difficult, and an injured bear is much more likely to attack you and inflict tremendous injuries. Not to mention the ethics of such a reaction. More often than not, putting a bear down isn't necessary because the methods of deterrence are very effective without resorting to lethal means.
You're off the a very good start in this objective of making associating the food source (chickens) unpleasant with the presence of the dogs. A hot wire is also very effective at causing an unpleasant association with the chickens.
I'll try to get some photos in a bit to illustrate how my run is wired. But the key to the hot wire being a successful deterrent is to (1) Bait the wire and (2) Keep the wire charged full time if possible. Baiting the hot wire with peanut butter entices the bear to interact with the hot wire in the most effective way. And keeping it on may actually prevent further attempts if my suspicion is correct that bears are able to hear the current pulsating through the wire, keeping them from wishing to get close enough again to the source of pain.
The reason I suspect bears may be able to hear the current is because of my own experience and that of my other neighbors seeming to have many more incursions when we've neglected to activate the wire.