Hi Someone
You say that you have 'barely met', but that means that you
have met ~ and, presumably, she knows that you have mutual friends.
Next time you
do see each other you could just start by giving her a big smile and simply saying hello, and introducing youself. You could say something like
'we met at ..., if you remember? Or
'Didn't we meet at ...?You could even ask
'Do you come here often?' ~ such an old-fashioned cheesy chat-up line that it might just be considered amusing, and break the ice.
You could offer to get her a drink, perhaps ~ soft or alcoholic, depending on age and circumstances ~ or something to eat.
You don't say how old you both are, which can be important.
You could chat about recent films, TV series, or hobbies, or sports ~ just be friendly and follow her interests.
Then you could ask
'Would you like to go to ... this weekend?' It could be a meal, or the cinema, or bowling, or whatever interests you both.
You should be able to tell from her reaction whether things are working out as you had hoped.
Be genuine; be friendly, be nice; be interesting; more importantly ~ be beinterested
Good luck
