Hi - just replying to get you some traffic, particularly as it’s your first post!
You might want to re-post on AIBU to get more responses, although it can get quite “boisterous” there and you might not like all the replies.
I understand where you’re coming from with your desire for a softly softly approach from the school - but actually I think you need to trust the house mistress that she knows her job and knows what she’s doing.
The school will have a policy on dealing with bullying (including for assessing potential bullying) and they will stick to that even when a parent asks them to follow their own ideas on what to do.
I would assume that the house mistress wanted to get your DDs point of view on what was happening so if there were any concerns she could nip it in the bud more quickly than “just watching” and then reporting back to you.
I know it’s hard but you need to trust the school to know what they’re doing and know how to help your daughter; so you need to let them do it their way.
That said, they should have told you that’s what they were going to do, and they should keep you updated. I think your best bet right now is just to ask for improved communication.
Good luck getting it sorted! I was bullied multiple times at school and nothing the teachers did ever made it better but my daughter’s school is amazing with this. I don’t know how they do it, but as soon as my daughter reported a problem to her teacher the teacher said she “put it into the system” and half an hour later the girl in question voluntarily apologised to my daughter. The teacher’s response when she called us to tell us was that our daughter really should have reported it sooner rather than being upset for days first.