It will cost you 2-6 dollars one way, and take you about 50-65 mins take the Red line to Metro center and get on a train to Ashburn.

The walk from the station to the terminal is 5 minutes in a warm tunnel.

2 dollars right now on the weekend, probably about 6 during the rush on a weekday. I checked out the trip the weekend the silver line opened as I fly international pretty often. The numbers Google maps gave agreed with my own timing of the route on the day I did it.