1) Be yourself, Try not to be nervous, after all you've been around her before and probably were not nervous about being around her before you found that she may like you.
2) Talk to her like a friend and focus on cultivating a stronger friendship with her. If there is a desire by both of you for something more it will happen over time, but don't be in a hurry to go straight from coffee to dating to marriage. Just start with coffee with the idea of getting to know her better. After all you may have coffee and find that aside from the art thing she bores you to death.
3) Have a next step idea. Meaning if coffee goes well, invite her to do something else with you, different art show next weak. Your favorite art museum, anything that's interesting to you that you think she might enjoy as well, or find out what her favorite art place is and ask her to give you a tour. Just make sure you are going to places and doing things she likes at least half the time.
4) If you can sustain this, it's called dating. Congratulations! Keep us posted.