http://www.mta.info/mnr/html/mnrmap.htm
) from New Haven to New York City, the ticket is like $13 (one way, off peak) if you buy it on the web. From New York, you can take the cheaper _dragon_ buses that run between Chinatown, NYC and Chinatown, DC. Those are much cheaper than Greyhound (like $20 one way, $35 round trip) but you need to get into NYC first.
http://www.chinatown-bus.org/
The entire thing is going to cost _$60 roundtrip....
Once you_re in the DC area, you can just use the Metro to get to wherever your final destination is...
http://www.wmata.com