Depredation permits are indeed available in may states for those engaged in agricultural pursuits. In fact, I have participated in depredation activities in commercial minnow/goldfish operations in the past. You must also realize...YOU WILL NOT BE TAKEN SERIOUSLY UNLESS YOUR INCOME DEPENDS UPON THE AGRICULTURAL ENDEAVOUR...in other words hobby beeks or "sideliners" (you got another "real" job) would probably not qualify. Also, other countermeasures must first be taken to thwart the nuisance animals' activities. In beekeeping with bears, at minimum, you would most likely have to have electric fences deployed unless you could prove it was economically infeasible (agricultural requirements and scale would be the factors).
Black bears fall under STATE game laws (unless on federal land) and would vary from state to state. The activities I know about were regarding nuisance animals at the FEDERAL level and those standards are much higher. The last thing anyone needs to be "caught" doing is taking any game out of season. Also, if you're going to "do it", I would suggest never discussing the issue and any countermeasures in any forums. Wildlife laws and investigations are no different than other criminal investigations, in fact, many times the legal thresholds wardens and wildlife investigators have to meet are LOWER than those of other law enforcement agents.