You don't need to wear a mask to be a woman of mystery! Take a cue from Angelina Jolie, who played a CIA agent on the run in Salt: all you need are two wigs and some creative wardrobe juggling.
What you need: A blonde wig, a black wig, a trenchcoat, and a change of clothes in a backpack. Every half hour or so, excuse yourself to the bathroom and change up your "look." No one will ever suspect your real identity! (If you actually want to go as Jolie's character, Evelyn Salt, give your friends a hint by carrying around a salt shaker.)