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I think it's entirely possible for it to be a Gender-Inverted Trope. I don't think there's much difference between a male version and a female version except that the latter is much more common. You might try Upper-Class Twit, but they're usually less malicious then simply, well, twits.
Edited by nrjxllGood, that means I won't risk accidental redundancy by making Rich Bastard a redirect to Rich Bitch, right?
Fiat iustitia, et pereat mundus.

Is there a Spear Counterpart to Rich Bitch?