The best way I've found is to do something selfless (which is not the same as "selfish"!). For example, give her a compliment in a way that suggests you are not after something more, and one that will get a response / start her talking.
Maybe something like: "Hi, I swear to you I don't usually walk up to women like this, but when you walked in here I was literally entranced by that fragrance you're wearing. So I just had to ask you before I leave, what perfume IS that?" (pray it's something exotic and not Ben-Gay...)
You can also throw in something funny like "I want to buy a case". Why, she asks? "I'm planning on spraying my entire house with it so I'll never forget you, why else?" (say this sarcastically, of course)
Unless she's got real attitude, it will start a conversation ...
It works because a) you've got guts, b) by saying "before I leave", she's thinking she has to act quick (assuming she's interested too), c) if it is exotic or unusual, rare, etc. she will love the attention - it's why she bought it!, and d) if you were about to leave, she may mention it "oh, look, your friends are leaving" ... you come back with "they can wait." (or something similar).
Net net: You are letting her know that you are humble, can give non-body-related compliments, and that for that minute or two you're entire focus in life is on her.
