In Minnesota, we have the right to kill any bear we feel is directly threatening our health/safety, whether in the house or outside on the property. I don't know if NJ has such a thing, but maybe you should check into it....
Heck, if you are allowed to use deadly force to protect yourself against bears, without having to first get a permit to hunt them, you could shoot first and say later that you truly thought the bruin was going to attack -- especially since it was ALREADY "in the house". Might take a bit of 'splainin' to the cops, but what the hey...and it just might help get the message across that the bears in NJ are more than just a "nuisance".