I believe the Georgetown Marriott is actually closer to GWU or Dupont Circle (in terms of public transport). Siliver Line Bus to Metro to Circulator bus toward Dupont Circle would still work (I think it's at the Rosslyn station though), but stay on past Georgetown until M & New Hampshire NW, which is right around the corner from the Marriott.
Alternatively I think a slightly faster way is to do Silver Line Bus to Metro and get off at the GWU stop, and walk ~10 minutes to the hotel, but this might be harder if you have a lot of baggage.
Its pretty close to dupont circle from what I have seen on the maps. I haven't been to dc in years. We each should only have a roller bag and a back pack so it wouldn't be too hard considering we just did a bunch of walking in thailand recently but I had to carry the bags since my friend couldn't carry her bag because of her sunburn so it was a nice walk in Koh Phi Phi from the ferry to the room with two bags strapped to me.