Discount busses are good, though they take a while. Be warned, though: it sounds like you're looking at Bolt. Last I checked, Bolt does *not* stop in Chinatown in NYC, so if you're connecting to a true Chinatown bus you'll need to trek across town to get to it.

This may be far enough in advance that you can get good rates on Bolt and the like and just go through Port Authority, though.