Time to update the thread. As of Saturday, you will have multiple public transport options to get to/from IAD.
1.
Fairfax Connector line 981/983 for to the Wiehle Metro Station for a grand total of $1.75 (30 mins to the metro)
2.
Silver Line Express for $5 to the same metro station (I imagine the ride won't be more than 15 mins), wifi.
3.
Metrobus route 5A for $6 (1h4m to L'Enfant Plaza).
If you have some time to kill at IAD and want to go visit the Smithsonian Air and Space museum, the 981/983 bus will take you there in less than 15 mins. See timetable above.