Live (until this week) not far north of DuPont circle. Have done this drive several times.
The only way to do it and keep your sanity is to pay close attention to the traffic on Google maps. GW parkway will be a disaster because (1) traffic on it, especially around CIA, and (2) crossing the river to work your way north to the circle.
Unless google maps traffic shows big problems, your best route would be Dulles access road to 495 north to Clara Barton, exit Clara Barton at the first exit to McArthur. Take McArthur in to Loughboro where you turn left. Sibley Hospital will be on your left. Loughboro becomes Nebraska, which runs into Mass ave. take a right on Mass ave.
You can expect very heavy traffic on 495 crossing the Potomac, a backup on McArthur at a one lane bridge, and a mess of traffic as you traverse embassy row on Mass ave. I'd expect a 90 minute driving time ex accidents but could be less, since the trip, except for beltway, is largely counterflow