Unfortunately, there is no airport-sponsored direct connection (that I know of).
For a cheap option, try this:
Washington Flyer Coach. You can then take the Metro to DCA
Washington Metro System.
This company may present another option, so they might be worth a call:
Super Shuttle.
If you need something faster, you could take a cab (about $40 - $45, last time I did it; it may be a bit more now that gas prices have increased).
FYI: to and from DCA, you are not allowed to move about the airplane cabin for the 30 minutes of the flight closest to DCA (i.e., if you are departing, you must stay seated for the first 30 minutes of the flight; if you are arriving, you must stay seated for the last 30 minutes). Something to keep in mind when partaking of pre-flight beverages (and especially more so for those of us cursed with small bladders!
) IAD has no such restrictions.
More unsolicited advice: If takeoffs from DCA are to the North, sit on the right-hand side (seat F); and if landing from the North sit on the left (seat A) for a spectacular view of DC – especially at night when all of the monuments are lit up.
