I have had a lot of experience with shy girls. The important thing to remember is that they have some issue affecting their social life. We all have issues we are working on, but there is this sliding scale of how badly it is actually affecting our life. It's up to you to weigh up how much of a problem her issue is for you, with all her good points. Often times it can be very much worth it
The biggest challenge you will have is copping her weird behavior right on the chin, being strong, not reacting emotionally to it, giving her time to become reasonable if need be, and then continue being positive with her. There may come times where you have to be firm, but be brief, and NEVER EVER get angry. The reason I say this is because shy girls can become really irrational and insulting while dealing with their issue, and at the same time, someone getting angry at them is the last thing they need. Also it can be hard to tell if you're angry. The best way to tell is how you feel inside. If you feel calm and indifferent about the outcome - you don't care what happens or what she thinks, or you're insulted or frustrated but willing to drop it and just do something else, you're fine. If you feel you really strongly need to make a point at all costs - you are angry, and you should just shut up and leave and calm down.
If she is ignoring your flirts, then stop doing them - she's not comfortable with them. Comfort is a big thing for shy girls. Instead attract her in other ways. Through your interactions and conversations throughout the day, show her that you care about her and are capable of looking after her, remembering what she likes, what she doesn't like, etc.
Soon you will find her adoring you and practically throwing herself at you.
Watch out for the kind of girl who moves real fast with the comfort stuff. Confiding her deepest problems with you if you feel it's too soon for that sort of thing, getting you gifts, opening up to you in a way that seems way too quick for her shyness, eg. showing you nude pics of herself - because at the point where you reach the seduction stage where she finally realises she's attracted to you, she'll go cold. She'll cancel on you and stop talking to you. She gets scared. That's where you have to take it easy and give her some space, but keep building comfort, and keep giving her the opportunity to get out with you, once in a while (but not as often as before).
Anyway with you sounds like she is already scared and you have to work on comfort.
What are your other interactions like?