Please don't think it's your fault. It isn't. It's a coping mechanism she learned somewhere.
I would think the best way to help your daughter is to make yourself emotionally and mentally available to her the best way you can. When I was harming at 13 I begged for the day when I could sit down with my parent(s) and be able to talk to them like friends and not have that "parental freak-out" over what I had done.

Just be there for her, and if she knows you are there for her, she'll be more likely to turn to you sooner rather than later.

Have you thought about writing a note to leave for her somewhere? That way she has the comfort of privacy but the option of knowing you're there for her?