>>33267166 (OP)>>33267513>Because I didn't choose to date her for her looks in the first placeThis is the real problem.
It can't just be her hair that is bothering you and if it is, then this is only the start. I think what is actually happening is that you're slowly realizing that despite her personality being great, you truly aren't very attracted towards her. Eventually you will start to resent her makeup style, clothing style, her laugh, and then her body.
Every time I've dated a girl who I wasn't 100% attracted to but she had a "great" personality never ended well. Every time it ended with me breaking up with them or them breaking up with me because I obviously didn't care anymore and self sabotaged the relationship.
If you really want her to change her hair style, simply say you think X style would look really cute on you. If she likes you, she'll at least try it. Now, if the new hair style includes either A) Growing her hair out a substantial amount and she's kept it short the entire time or B) Her hair is long and you want her to cut it, she probably won't oblige unless she herself wants to do it.
Though, if a girl really likes you, she'll definitely do what you want. I told a Korean girl that I'd only met up 3 times with that I like thick front bangs. She asked if I had scissors and went to the bathroom and cut her hair into bangs. When I met my Asian ex girlfriend she had chin length hair, I told her I think she'd look great with long hair. She grew it out until it almost reached her ass before we broke up and then she cut it. Another Asian girl who always shaved her pubes because she didn't like the feel of a bush agreed to grow it out for 6 months until after we came back from our trip. She promptly shaved it once we returned as her push was like 4-5 inches long.