Directions from BWI via Train/Metro.

You can take either the MARC or AMTRAK trains from BWI to Union Station in DC. This will be ~$7 and take about an hour. This will require getting on a Shuttle Bus at BWI to take you to the airport train station.

Once at Union Station- Take the RED Metro line to DuPont Circle for access to Westin, Jury's etc.

Be sure to check out train schedules for the return trip as things are sometime weird on Sundays. Remember that you can take AMTRAK or MARC.