This ride starts in Old Town Alexandria, VA just south of Washington D.C.
It is best to plan very early so you can book a non-stop flight for ease of traveling with bike boxes. Bike boxes under 50lbs count as first check bag on most airlines. Southwest charges much more and lost my bike last trip. Make sure you have an airtag in your bike box so you can see it get on the right plane when transferring. When my bike was "lost" by Southwest I could tell them exactly where it was sitting at another airport.
It is highly recommended to fly into DCA Reagan International Airport.
From Termial 2 there are 2 pedestrian bridges that lead to the north and south ends of the Metro Station.
The Blue and Yellow lines alternate about every 6 minutes going southboud.
The fare is $2.50 one way. Buy a ticket or card at the station.
Take the metro 6 minutes to the third stop, King St. Old Town Metro.
Below is the link to the metro trip from DCA to King St.
https://www.wmata.com/schedules/trip-planner/trip-planner-results.cfm?locationLatLng=38.851242%2C-77.04023149999999&destinationLatLng=&first-form=&location=RONALD+REAGAN+WASHINGTON+NATIONAL+AIRPORT+%28DCA%29&destination=KING+STREET+METRO+STATION&travelby-trip-planner=BCFKLRSTX123&arrdep-trip-planner=D&hour-leaving-trip-planner=5&minute-leaving-trip-planner=05&period-leaving-trip-planner=PM&month-leaving-trip-planner=4&day-leaving-trip-planner=1&route-trip-planner=T&walk-distance-trip-planner=.75
You can also fly into Dulles Airport.
From Terminals walk through the Dulles Tunnel under the parking lots to the Metro Station.
The Silver Line leaves every 15 minutes and takes 45 minutes to get to the Rosslyn Metro Station in DC.
The fare is $6.75 one way. Buy a ticket or card at the station.
At Rosslyn Station you have about 5 minutes to transfer to the Blue Line.
The Blue Line takes 18 minutes to arrive at King St. Old Town Metro station.
Below is the link to the metro trip from Dulles to King St.
https://www.wmata.com/schedules/trip-planner/trip-planner-results.cfm?locationLatLng=&destinationLatLng=&first-form=&location=DULLES&destination=KING+STREET+METRO+STATION&travelby-trip-planner=BCFKLRSTX123&arrdep-trip-planner=D&hour-leaving-trip-planner=5&minute-leaving-trip-planner=05&period-leaving-trip-planner=PM&month-leaving-trip-planner=4&day-leaving-trip-planner=1&route-trip-planner=T&walk-distance-trip-planner=.75
The reasons for flying into Dulles are possibly cheaper flights.
The reasons for flying into Reagan are (1) shorter metro trip, (2) no tranfer on the metro especially with bike boxes in tow.