My girlfriend lives in NY so I've taken the Fung Wah bus b/w Boston and NY a lot, and I have to say, all in all, it sucks a$$. It's dirt cheap, but on two occasions the bus stalled in CT and we had to wait for a replacement, which added 2 extra hours to the trip.
The only advantage is cost, but you still need to get from South Station (in Boston, where the bus drops off) to BU, which wont be easy by train, since you have to switch at least two lines, and then walk another mile to get from the Mass ave station to the Hampton (I'm presuming youre staying there since theres no other option around). So, you're probably going to get a cab, which is gonna cost at least $15, probably $20. If you catch a Jetblue sale fare, it would be much better since you can have the hampton shuttle pick you up for free at the airport.