Well, considering you've picked a rather obscure character, there's isn't much to designate her. If I were you, I'd be prepared to explain over and over all night who you were. I mean, what does the daughter of the king of Crete look like?
And it wasn't like she had a happy life with Dionyus either.... He found her pregnant by someone else, and then she was killed by Aphrodite on the island of Dia over something that Dionysus said.
I think you'd do better going as one of the Dionysian accolytes, a Meanad. You could smear your toga, face and hands with fake blood and dance around the god, singing his praises all night and pretending to attack other male guests at the party periodically.....