The drive from Dulles to the beltway, whether by yourself or with a cab, uber, bus etc. is easy. The problems begin there. Driving via anything during PM rush hour to downtown is torture. It's even worse with the cross town drive to Union Station. Don't do it. The problems are (1) inner belt is a 10 mile crawl from Dulles access road to I-95 north. (2) driving into the city is tough because of rush hour one-way and lane restrictions for those leaving the city.
The only reliable way is to take the the Wash Flyer to the West Falls Church Metro station, then Metro to Union Station and Amtrak to Phil.