There's a very nice bar on the corner of I Street and 19th--Elephant & Castle. There's a much smaller place on the same corner, across the street. Looks like the current name is just 19th, and the reviews are so-so.
Alternatively, there are tons of small, funky bars in DuPont Circle.
If you really want to WOW her and don't mind paying out the nose, then there's the bar in the basement of the Hay-Adams Hotel, near the interesection of 16th and H St, just across Lafayette Park from the White House. Never been there, but I've read that it's very quiet, very "London Club" in its decor, and drinks are, like, $50 each. Or something. Whoa,
here it is. (I should research first and write second!)
Good luck! May her beauty be eclipsed only by her wit and emotional stability (the trifecta).