You should be able to do it - although you might have to take a taxi in one direction or the other. On weekends, the 50 cent shuttle leaves the airport 10 minutes past each hour starting at 11:10am - and leaves Udvar-Hazy at 30 minutes past each hour. Taxi fare should be around $13-$14. No problem getting a taxi from the airport to the museum. But you might have to wait for a taxi to be called from the museum for the return trip - check with the information desk inside the museum.

Note that the "real" shuttle will be arriving at Udvar-Hazy next week. A big series of celebrations is planned.

Here's a link to the 50 cent shuttle schedule: http://www.vatransit.org/route%20maps/Dulles2Dulles.pdf