Something I have heard that was done in the past for inviting their "Crush".. they would go to a store and buy those "Crush" sodas.. then attach a small invite to the soda can.
The girls would exchange "Crushs" and give the sodas to the guys they had a crush on. (Example, I will give Jane's crushes their invite/soda and Beth will give my crush their soda/invite) so it's a mystery who invited who.
Something else you could do is a "Mystery Date" theme party... Maybe go with a 70's/Scooby Doo theme ? (I'm not too wild about 70's colors.. but it's an idea
) Maybe if your chapter makes shirts for their events you could have the Mystery Bus on the back for a Mystery Date party?