Knock on her door and ask her if she's seen a cat that looks like Church from Pet Sematary, your beloved little kitty got out of the house. If you manage to strike up a conversation after that, you can get to know her. Chicks love cats, they think guys who like cats are sweet, and as long as you don't puke on her like the kid from South Park does on the chick he likes or totally stumble over your words, you've at least met her and the door's open for further conversation.
Good luck!
