OP, I get what you are doing and it feels like you're doing your all and your best, but as a survivor - yes, it feels like that - of bullying including sexual bullying - let me tell you that you are getting it wrong.
You're thinking about the here and now. What she wants now, what she feels up to now, what works for your lifestyle now, sorting out what's happening now. But the worse part of being bullied is actually not about what happens at the time it occurs, it is afterwards, it's about the adult life of the victim.
Of course your DD doesn't want to go to the police, to tell on her peers, to make a fuss, to change schools. So you, loving mother that you are, heed these wishes. But this is a scenario where you have to insist on 'Mother Knows Best' and do what's right, not what she wants, not what works in the short-term. By not making her talk to the police, to be more proactive, you are teaching her, as surely as anything she leants at school, that she must minimise abuse, that she just needs to accept, albeit with a bit of fuss, what happens to her. These are two major facets of the mindset of domestic abuse victims. It is more common for female victims of childhood and teen bullying to go on to abusive adult relationships than not, not just because of the damage that the bullying does, but perhaps even more importantly, because their parents don't handle things properly and give them unconscious messages that they somehow deserve it, or don't deserve protection, or should just not make a fuss.
The option you need to take is the hardest one. You need to push this much, much further than you have done. You have to be cruel to be kind. You are the parent here, and she is only a child. 13 is still very young. She doesn't get to have the final say on matters where she just cannot understand the bigger picture and long-term implications. And I say that as a right old hippy mother.