There are a few things to keep in mind if you are taking public transportation from BWI to DC and decide whether to take the bus or the train.
If you take the B30 bus, you can catch it at one of two stops at the terminal. The bus will take you to the Greenbelt Station (which is suburban stop on the DC Metro system), and you will need to transfer to the Metro. Chances are, however, that your hotel will not be along the line that serves the Greenbelt Station, so you will likely need to transfer trains and ultimately walk to your hotel from your final stop. Information on the bus (including timetables) can be found at www.wmata.com/bus/timetables/md/b30.pdf.
If you elect to take the MARC train or Amtrak to DC, you will need to take a shuttle bus from the terminal to the BWI Train Station. The terminal and train station are at separate locations (and only a few minutes apart), but you cannot walk from one to the other. If you plan to take the MARC train, take a look at the Penn Line Southbound schedule and see what works best for you. The MARC or Amtrak trains will drop you at Union Station in DC, and you can then grab a cab to your hotel or jump on the Metro from the Union Station stop.
Where you are staying and when you are arriving will determine which option is best, but taking the train is probably going to be the most efficient way for you to travel by public transportation.