She is shy around other people but not around me. I think she likes me but I don't know. How should approach her to ask her out? What should I say to her?
Just wait for the right moment; You'll know when that is trust me! It feels like you like her so much that you couldn't possibly feel any more for her! This is the perfect point because chances are she's having a good time as well - just casually ask her something like "You should hang about in town with me and my friends sometime"
(HINT- When you're asking this question to this girl for the first time it's best you add words like 'friends' as it's less off putting - and I wouldn't recommend saying "Wanna come to town with me on Saturday?" As it's so final and obvious - You should probably leave that to the second date :)