NYC transit bus drivers should be used to bicycles by now, so the thing to do as one comes up behind you is hold your line and speed, and let the driver decide if he has the time to complete his pass before his next stop. If he sees you as a steady rider he'll plan accordingly and you won't have issues. However space on NY streets is limited, and there's not much difference between your speed and his, so you might find yourself riding a narrow lane with the bus walling off one side. This has never bothered me, but if it does you, simply slow slightly and let him slide by.

The bigger issue is managing passing stoppd buses which may be ready to pull back out. Some drivers are excellent about changing from 4-way flashers the use when stopped to the left turn signal before pulling out, but some not so good. As I pull up to a bus I try looking to his right and estimating how many passengers are left, and if I'll complete my pass before he pulls out or not. If I suspect he's getting ready to pull back out, I slow and stop or stay behind him, on the side not belching diesel smoke.

On one of my commuter routes home, I ride at just about the same average speed as the local bus, and we play leapfrog for miles. I make it a point to know the drivers (always the same few) and them to know me, and we work together so it works. They know they can't pass me coming to a stop, and I don't pass them as they pulling out.

BTW- where possible in NYC try to choose one way avenues vs. two way. This will let you keep left and avoid the bus traffic entirely.