If she cares about you she cares about your stutter. Stuttering is a part of you that you can't really hide. I know it sounds frightening but I think you should talk to her about your stuttering. Try to explain it to her what it feels like, what you have to deal with in your everyday life. Believe me, non\-stutterers don't even realize that simple tasks like a phone call or ordering food can be such a struggle for us. If she cares about you, she will listen. And I'm sure both of you will feel more comfortable afterwards.