She probably thinks your stutter is cute and makes you vulnerable and genuine. My past girlfriends all said my stutter was one of the things that attracted them to me. I also went to my high school reunion and was told that a few girls I was unaware of thought I was interesting and attractive even though everyone knew I stuttered. Your stutter is not a turn-off. Your lack of confidence is more of a barrier that you stutter is. Work on building your self-confidence. There's no reason for your stutter to hold you back when so many women think your stutter is actually attractive.