If you're taking Amtrak, just go to the closest train station.
It will be about an 8 hour train trip minimum on regional or about 7 hours on Acela (twice the price to save an hour). It's about a 90 minute flight from BOS-BWI, and a cheap fare I found in the middle of April was around $120 round trip. Driving would be the cheapest if you split the gas, assuming gas stays cheap, and would be 7-8 hours with no traffic, but could be up to 10 hours in I-95 traffic, plus you would have to park the car in DC which could get expensive. If you fly, your total travel time will be about 1 hour to get to BOS, 1 hour in BOS, 1.5 hours flying, and 1 hour to get to DC from BWI for a total of about 4.5 hours to get to DC. The cheapest Amtrak fares I have seen are about $170 round trip before your discount, so flying is the best way to get to DC, unless you enjoy spending $50 more to sit on a train for 8 hours. Forget about the Acela if you're paying for it yourself, it's $70 more than a regional train and doesn't save much time, I'd only take the Acela on my expense account. I'd do Amtrak if it's January and I really needed to be in DC at a certain time, as flights may get cancelled if someone sees a snowflake, and Amtrak is reliable when there's a foot of snow, but in April, snow is unlikely.