You're already friends with her - the stutter is bothering you and not her. Do the two of you do anything outside of school together, common interests? It can be as easy as asking her if she wants to get ice cream on Friday night, or see a movie. Having, or at least portraying, confidence will go far in life. You don't have to ask her out to a candle-lit dinner, just start with something simple that you both enjoy! I would personally stick with something where there are other people around as you could always resort to people watching together if you find you have no idea what to say. Is going to the mall and walking around together still a thing these days? ​