The free shuttle is long gone. However, you can take a public bus.
https://airandspace.si.edu/visit/mal...-locations.cfm
From that page:
From Washington Dulles International Airport to the Udvar-Hazy Center in VA:
•From Ground Transportation, take Fairfax Connector No. 983 one stop to Steven F. Udvar-Hazy Center.
And here's the link to information on the route.
http://www.fairfaxcounty.gov/connector/routes/983.htm