It is faster, by far, to take Amtrak between Baltimore, MD, and Washington, DC. None of the major airlines even offer direct service between these two cities. The fastest flight time I found using a random date was 3' 59", and that includes a stop in Boston, for $476.
Amtrak has dozens of trains per day operating between these cities, as does MARC, the Maryland / Washington D.C. commuter rail system. A typical Amtrak train can make the trip in around 38 minutes for around $15. MARC can get you there cheaper, but it will take just a little longer, as they make more intermediate stops.
To check on schedule and fare information, or to make reservations, visit Amtrak's website at www.amtrak.com, or call the Amtrak Reservation Center at 800.USA.RAIL.