In my area bears are rare, but in the east there are many of them and people sometimes hunt them when there are quotas. Small indigenous peoples hunt without quotas. One of them once treated me to a bear stew baked in foil, quite tasty.

If I had the opportunity to hunt, I would take #13-12 just in case, if for cutting carcasses, then a hatchet and 11-4.5 or 20 Ward Gay

In general, the problem of maintaining the balance of predators and herbivores is very difficult, unfortunately.