Try classes at Glen Echo, waltztimedances.org or Gottaswing.com if you want more options. Also places like chevychaseballroom.com offer many types of dancing styles. There's a Latin dance place on Georgia Avenue in DC (Sylvia Dances or something).
I've only attended one class from among the ones I listed above. It was so fun I'm planning on more.
So I've done a little investigation and here's what I've gleaned. Most dancing classes are fine for singles. Both single men and women show up. Then you rotate partners every 5 mins or so, so everybody gets to dance.
I don't know who attends rec center classes. The class I'm attending attracted a range of ages from young couples getting ready for their wedding to 40s, 50s, and older. I think there's a 70-something in our class, and she's doing great.