"This is a 6 year old. Who is likely still receiving help for incidental personal care from adults in her life when her parents are absent, such as staff at school, Rainbow leaders and Gym class instructors."
My six year old can change into his swimming costume and (I think) PE kit.
But even so, he may need help. "It is highly likely that she will ASK the adult her father trusts to help her with 'putting on her tights' or 'brushing her hair." That is not the same as sleeping all night in the same room, is it?
The thing about a bedroom is, it can be a kind of 'sanctuary'. A place to go and cool down, quieten down etc. If it is a room shared with two adults it loses some of that.
I think it is all very well to say that the other parent can do what they like as long as they are not harming the child, but there are degrees of 'harm'. Assuming all was well and fine and no one minded now, great. But what if the dd (or any child in similar position) did mind and said so to her mum? Would the mum just 'It's nothing to do with me.' I don't think so.
What if the shared room continued until the child was 9, or 10 or 11, or older?
It may be fine and harmless, but both parents can raise concerns if they are not happy with the way things are. I really do wonder (rightly) how any woman's ex would like the idea of their ex's new partner, long or short-term, sharing a room with their dd. I think they would have something to say about that (and I would agree). But this child has her own room at her home.
The dad has her with him 50% of the time so his home also becomes her home.
I do tend to agree with user1483300717 that if I was not happy I would not leave it at that. But if the OP is happy that is fine. She knows the dad and can get to know he girlfriend.
One other 'concern' I would have is that the dad and girlfriend would be all lovely dovey around the child and this would be hard for her. When people are new to a relationship they tend to be much more open to public displays of affection. Which kids seem to find quite embarrassing!
For this reason, and many others, I would want to meet the (relatively) new girlfriend (and see what she is like around the ex). I would want to know all I could and I would try and be friends with her.
It may even be she is more of proactive in getting things good for the child than the ex, for all kinds of reasons (like maybe wanting her own privacy too!)
OP I do hope all will be well. 