Reagan is closer but Dulles isnt that far.
http://www.bethesda.med.navy.mil/visitor/get_here_and_park/Directions_Maps_Transportation.aspx
Area Terminals
Reagan National Airport
1. Driving: From the Airport, exit north on George Washington Parkway. After about 2 miles, you will see but do not take a left exit for Memorial Bridge and Arlington National Cemetery. Be sure to bear right and continue on GW Parkway, which follows the Potomac River on the Virginia side, for approximately 12 miles. From right lane, exit onto I-495, Capital Beltway, heading north to Maryland. You will be on the inner loop of the Beltway. Take Exit 34, Rt. 355 South, Wisconsin Ave., towards Bethesda. Get in left lane. Cross Cedar Lane intersection; at first median crossing (no light), turn left into the National Naval Medical Center. At the guard station, show ID. From here you will be directed to parking.
2. Using METRO (subway): Take Yellow Line towards Mt Vernon Square. Exit at Gallery Place METRO station. Take Red Line towards Grosvenor or Shady Grove. Exit at Medical Center METRO. At top of escalator, turn right and cross Wisconsin Ave. Show ID at guard stations. Approximately 35 minutes.
3. Other ground transportation options from National.
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Dulles International Airport
1. Driving: Drive east on the Dulles Airport Access Road for approximately 13 miles. Exit onto I-495 North, the Capital Beltway, towards Maryland on the inner loop of the Beltway. Take Exit 34, Rt. 355 South, Wisconsin Ave. towards Bethesda. Get in left lane. Cross Cedar Lane intersection; at first median crossing (no light), turn left into the National Naval Medical Center. At the guard station, show ID. From here you will be directed to parking.