Meeting a client over coffee today. Who pays?

I'm a freelance professional violinist who plays for weddings and other events. Today I'm meeting with a future bride (who has already hired me) to discuss specifics for the wedding over coffee.

Who should pay? She initiated the meeting, but she is the client. Should I just get there early and pay for my own, or would it be rude to order before she arrives, and not pay for her?
I don't mind paying for her coffee at all. I just want to know what the proper thing to do is, I don't want to make her feel awkward. If it makes any difference she is also at least a few years my senior (I am in college).

You should pay for it, she's the customer here allowing you to play her wedding. I'd want to give her a great impression& be as nice as possible, she's a bride who's probably very stressed about her wedding planning right now- it's an extremely nice gesture and it's not as though it'll be all that expensive. Not to mention, it'll give her positive feedback and will possibly make her want to tell her friends about you. It could help you get more clients. So looking at it, something as simple as buying a coffee for someone can help you expand your clientele, I'd buy it!