The 119 and 125 make lots of stops on their way to PABT. There's also the 123, which starts at Christ Hospital on Palisade Ave and goes north to PABT from there.

If you live downtown, going up to JSQ to catch these buses doesn't make a lot of sense. It'll be faster and cheaper to take PATH to the city and transfer to the NYC subway if you're going farther uptown. There are a few 126 buses that start/end at Hamilton Park in downtown JC if that helps.