Have I misunderstood something here, so many replies saying to soon, focused on "new partner" as if you have only just met him, I thought I'd read it was 1yr now with partner & that he met DD 6 months ago? So new partner in the sense of new since split from husband but not new as in just a few weeks in.
First don't get focused on the many posts saying, it's because she feels scared, yes it's a possibility, but as you say she likes him & she has now known him 6 mths - which 6 mths is a longer time for a younger person, than us grown ups, it's less likely fear. It could be fomo, it could be just the change of routine - which is more likely taking into account her sleeping in your bed, this could go on to create a fear if not handled thoughtfully.
I would suggest encouraging her independent sleeping when your partner isn't visiting, so she doesn't connect him to being the reason she can't sleep with mummy, then giving her a reason to begin to dislike him, or create a fear - imagine a child's mind "mummy loves him more than me" scenario.
Your partner not having children, will not understand how parenting isn't so black & white & the emotions felt as a parent around any issues. Remind yourself of this & know that all you can do is explain to him why she has slept in your bed, why you can't just simply say "no" explain why it's a process & how you will deal with it - the importance that DD does not see him as barrier in hers & yours relationship, or see him as more important than she. You can also explain to him, that you at this time, you don't feel he should be telling you how to parent, he is not her father, does not yet know her well enough & he does not have his own children to pull on any experience, this does not mean in the future, should you become long term, move in together etc, as you all know each other better, that he will never have a say (should that be your choice)
This is a really good time to gauge the type of person he really is, beyond the new partner honeymoon period where it's just about meeting up & having fun.
Back to the bedtime & any other changes that may come about as your relationship with your partner progresses, have a look at social stories. These are geared towards children with autism, but I have found many coping strategies for ASD, can work excellent for NTs too. Basically it's just a story you put together that breaks down a process, in your case, going to bed, in her own bed. You can use, words, pictures or photos, to do it, just do it in the way that you know will work best for you DD.
Hope it all works out for you