A few pieces of advice.
1) You need to accept reality. The chances you will have any real relationship with someone you only know on Instagram are pretty low. Most likely this will never never even meet in real life.
2) Even if you meet her you might not have any chemistry in person. You may not like her once you meet her, or she may not like you. Right now all you have is a fantasy... who knows if it could even work.
3) That being said... there is nothing wrong with trying. It is always good to take chances in life. Once in a while you get lucky and something good happens.
4) I would recommend the direct, honest approach... because if someone on social media were interested in me, that is what I would want. I would just say "hey I think you are cool, I would love to get to know you in person. Maybe we could have coffee or lunch".
That way you are opening the door without pressuring her and without it being weird. She can either accept your invitation or not... when people feel they have a real choice they are more likely to say "yes". By inviting her to coffee or lunch, you let her know that you understand that it isn't going to be serious at first... it is just an way to see if there is a connection.