Okay, i'll post one of my favorite day game openers:
if she's sitting down, you walk almost past her, if she's walking, you stop her.
then simply, "Okay, look... i have to ask you quick where you got that necklace/those shoes, those earrings. i'd love to get one/some like that for my girlfriend."
she answers and you go into some normal conversation.
if she asks you about the gf at any other point, you just tell her that you don't really have one, but you didn't want her hitting on you and trying to pick you up so you had to lie.
actually, you can use that anytime you use you having a gf as a disqualifier.