Not sure where you are but here in the California Sierra foothills bears are a common pest for chicken owners. Ive had two nearby friends lose birds to bears over the last few years. Worse, the damage the bears do while busting into a run or coop to get at the birds.
I've avoided bear predation (at least of the chickens) courtesy of a large 8' high fence that surrounds the couple acres or so that the vineyard and chickens are in. Not sure if your electric fence will suffice to keep out a determined bear, but here's hoping so.
Here in CA it is possible, but not necessarily easy, to get a depradation permit. The CA DFW first tries to get the homeowner to take all reasonable precautions and to dissuade the bear from coming back. if they don't g away, and there has been real damage (including loss of livestock), then they will give you a permit to shoot the bear. But then county ordinances apply - some folks live in areas where a hunting rifle wouldn't be allowed. You may need to check into your state and county.
It may not be financially realistic, but a strong wildlife fence may be your best long term solution if the electric fence doesn't do the job. One thing is for sure, the bears will keep coming back until they can no longer get an easy chicken dinner.