Washington dc: how to get to Georgetown University from the bus station?

Unfortunately the metro doesn't take you directly to Georgetown. If memory serves they Greyhound station is close to the New York Ave metro station and the Union station metro station, both of which are on the red line. From there you can get a metro train to Du Pont circle (also on the red line) and I think there's a bus that goes from there to the school. If not it's a mile to a mile and a half walk. Contact the school and they can tell you about a bus and how best to get from one to the other.

The DC Circulator bus runs from Union Station (a 5 minute walk from the Greyhound station) to Georgetown.

From the Greyhound station walk 0.5 miles south to Union Station (a big train station). Take the Red Line Metro (subway) in the direction of "Shady Grove." The 3rd stop will be "Metro Center" a convergence of 3 subway lines. From there either get on the Orange Line in the direction of "Vienna / Fairfax" or the Blue Line in the direction of "Franconia-Springfield" (for your trip, both trains will be using the same track so it doesn't matter which one). The 4th stop is "Rosslyn". Then take a cab or walk 1 miles due north (over the river). This is about 1 mile shorter than walking from Dupont Circle.