There's no need to go all the way to the zoo. There's a path up to Calvert St. (which is one block south of Woodley Road) from the Rock Creek Trail, or you can also ride on the adjacent road which is basically an exit from Rock Creek Parkway up to Calvert St. & Connecticut Avenue. I don't know if it's signposted, but the exit is just before you go under the Taft Bridge, aka Connecticut Avenue Bridge. wikipedia has a photo of this very pretty bridge. Note the distinctive double set of arches:
http://en.wikipedia.org/wiki/Taft_Bridge

Be warned that it is a very steep ride up to Calvert Road, however it is quite short and is easily walkable, if necessary. Type the hotel's address into maps.google.com. It shows the road exit as being 24th st. Go all the way up 24th to the intersection with Connecticut Ave. I'd suggest you walk a few yards on the sidewalk on Connecticut to get to Woodley Rd. rather than ride in the middle of Connecticut Avenue to turn left onto Woodley.