I'm not even joking here... I'm a firm believer that if my pets don't like someone then there's a reason for it. They're more insightful on body language than we are. I would have to seriously think about any girl I was dating if my pets didn't like her.
How does your girlfriend act around your cat? Does she love cats or is she kind of stand-off-ish? If Millie usually likes other people then it may be your girlfriend's approach.
If Millie has had bad experiences with anyone else in the past (like an over-eager child or hateful housekeeper) then there could be something about your girlfriend that's making her remember that experience... same perfume or pitch of voice, something like that. If your girlfriend wears something of yours that makes her smell like you, it might soften Millie up a little.
Otherwise, it really might just take some time for Millie to warm up to her. Having your girlfriend help out with feeding or giving treats is definitely a move in the right direction.
One other thought... I've always heard that when a cat presses his forehead to your forehead then it will leave a pheromone scent that other cats will recognize and know that you are someone to be trusted. If she has other cats in her life, then petting them and encouraging them to press their forehead to hers (not forcing, of course, just encouraging it) could possibly help. That sounds like voodoo to me, but hey, it can't hurt to try! lol