Introducing new cat to bunnies

We recently adopted a new cat. She is older and quite calm and the rescue had rabbits which she would happily ignore.

My bunnies know what cats are already and there were cats at the rescue they came from and our holiday boarder has cats. Neither seem worried by cats in general.

Our new to us cat has lived in the kitchen for the last 2 days and is desperate to go upstairs because she isn't allowed. The bunnies currently have a bedroom and can access our room and upstairs hall when we are at home. I know they can smell each other but I could do with some advice about cat coming upstairs?

I know she hasn't shown aggression or interest (and she has few teeth) but I would never leave them alone together!

So, what would anyone do next? should I let cat come upstairs supervised when bunnies are shut in to get them all more used to smell? I worry that bunnies become taboo for cat and it's then the only thing she wants to do is go near them. What would you do?

I'm not sure on the best approach to be honest. I have a cat (Smokey) who has seen my outside bunnies from outside their run. We had Smokey before the rabbits. Boots, my indoor bunny is free range in his own room when we aren't at home, when we are at home we let him out to free range elsewhere. Smokey is quite confident normally but not where Boots is concerned. I think it confuses Smokey because Boots just runs at him, and he finds this approach a bit too much in his face! When Boots is asleep or having snuggles with us Smokey is still wary. This morning Smokey was in the living room, he went to a box that he has claimed as a bed :lol: and laid down in it. Boots was on the rampage, so I fed him a bit of banana near to Smokey's box so they were close to each other for a while. Basically though, I would never leave them together unattended, I'm always next to Smokey just in case.