You can take the B30 Bus from BWI to the Greenbelt Metro Station (Greenline)

Or, you can take the Marc train from the BWI rail station to Union Station in DC. There are shuttles outside the airport. Look for the ones that say Amtrak/Marc Rail Station. One note: The Marc train doesn't run on weekends, but you can take an Amtrak train down in the schedules work. You might want to check here to see if the train option is a good one for you:
http://www.bwiairport.com/ground_tra...on/marc_train/
www.amtrak.com


You can also find some more info at the WAS airport forum - http://www.flyertalk.com/forum/showthread.php?t=573731