I would simply try to strike conversation, not being too specific at first that you want to know her. Just say hi, try to start with small talk, then introduce yourself by name and go from there. When you feel she may be ready to leave you could say, "It was a pleasure to talk to you // I enjoyed talking with you, would you like to keep in touch? I would like to give you my email/phone, could I have yours? Would it be OK if I call you sometimes?" But first give her a chance to get to know you a bit, and only offer to keep in touch if you have an indication that she enjoyed talking with you and you know she is single.

Hello In the UK you wouldnt use miss or madam with someone you know or dont know. Instead you would just say something like the following; Hello nice to meet you I am... whats your name or How are you its nice to meet you. Or Hello its lovely to meet you whats your name, or good to meet you is also ok. Excuse me I'm ... whats your name please? A slightly more formal way of saying hello but it also used informally is Good afternoon/evening, I am pleased to mee you. A very informal way would be Hey, how's it going, nice to meet you! This is the normal greeting. It would be the same whether meeting a girl or boy or man or woman. best wishes Gillian