The Metrobus # 5A runs hourly between IAD and L'Enfant Metro station (about 2 blocks from the National Mall and all the museums) for $3 each way (exact fare required). They take about 45 minutes for the express run (just 2 or 3 stops) - and it leaves IAD from curb 2E (where all the shuttle buses are). Departure times are at about 30 minutes past the hour at each end.

And I second the message above about spending time at the Udvar-Hazy building of the Air & Space Museum. Opens at 10AM. Actually on IAD property, but you need to take cabs both ways ($12+ each way).