The best numbers I can get right now on the NJ Bear population are that for the area designated for a hunt, there are about 7,000 Bears. The initial plan (again, in NJ these things change minute by minute) is to allow Shotgun and Bow hunting with no bait or hounds. In NY, this would make the odds of getting a bear about 1 in 5. That means with 10,000 permits issued, they would probably get about 2,000 kills reducing the population by about 28%.
I don't know yet if there will be ANY permits for out of state hunters, but I would imagine there must be. Given New Jersey's firearms laws there probably aren't 10,000 active hunters left in the state.
Let me be perfectly frank....from what I know about New Jersey, none.