From the Salk's International Airport Transit Guide:

Washington Flyer to West Farms Church Metro Station every 30 mins: 6am-10:30pm M-F; 7:30a-10:30pm. Trip is 17 mins. Cost: $8.

Transfer at West Farms to Orange Line Metro $1.65. 20-25 mins to downtown stations.

If you have the time and NOT too much luggage this might work for you. But a minimum 45 min trip, I don't know.

If you go this route please post a report on how it went.

I normally take a cab (most of my trips to D-C are for business) or take the dreaded SuperShuttle.