imo making jokes about her 'bf' is as cheesy as asking for the time or saying "nice weather aint it?" as an ice breaker. ask directly or ask a friend.
asking directly is fine, just don't be an ass about it and you should be able to get the answer you of which you seek
I wouldn't stalk her. It can turn ppl to jealousy and can lead to obsession. So ask her direcly, but casual conversation.