How would I handle it?
By not Bull sh!tting in the first place. Think about it man. The Pickup Community isn't a secret any more. I know just as many girls who have read "The Game" as I do MEN!
In addition, women are generally pretty intelligent. They KNOW when you are using a canned pickup line.
Try saying hello, and build rapport and conversation from there. Leave the pickup lines for later, but come up with more original or intelligent material. Trust me man. I've been there. You'll save yourself a lot of hassel.
Now, if you insist on making life difficult by using stuff like the jealous girlfriend opener, the very very best way to deal with a chick who calls you out, its to be 100% sarcastically honest about it. Just admit to it, and pretty much ask her "so what?". Its your best hope. Again; I've been there. In fact I have personally had success by purposely including an admission of guilt in with my opener..the fun honesty is refreshing to women and actually lowers their guard.