If you want to use the Mount Vernon Trail, you can cross on the 14th street bridge. There is construction on the trail, so use the detour to head north. There is a switchback ramp north of the Roosevelt Island parking lot the takes you to one end of the Key Bridge.

Faster would be to take the road around the Jefferson Memorial, along the river almost to Independence Avenue. At the little circle with the monument in the middle, switch to the trail along the river (extension of the Rock Creek Trail). Past the Kennedy Center you can get into Georgetown several ways - thru the boathouse parking lot to the Washington Harbor boardwalk, take the trail left under the highway to K Street, left on the C&O, up the ramp to M Street or up the next ramp to P Street.