I think that the days of having to wear one's hair up to look professional are over. Most of the time, I suspect your clothes differentiate you from the students. I'd take your cues, though, from the other teachers, if you are really worried. I had a teacher in high school with gorgeous hair longer than yours that she wore down all the time. She was a dance teacher, so perhaps that gave her more leeway, but I would think the same flexibility would apply to a music teacher.
Steer clear or headbands, though. They definitely make one look younger.
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Steer clear or headbands, though. They definitely make one look younger.