One issue is that you are introducing a pullet to hens. Mature chickens outrank immature chickens in the pecking order and some aren’t shy about enforcing those pecking order rights. As you saw, some are more aggressive than others. I don’t know how much room you have either. Normally immature chickens avoid mature chickens because that pecking is so common. I’m not talking about the coop space in isolation or the run in isolation but how much room is available when it is needed. And I’m not talking about square feet per chicken. I’m talking about can the pullet get away if she is attacked and avoid the others so she doesn’t get attacked again.
Another issue is that chickens are social animals, they like to be with other chickens. Your pullet is attracted to the other hens yet she gets picked on when she gets close. But she needs to avoid them to keep from getting picked on. This is often a reason introducing more than one at a time is often beneficial, they can have company without it being the hens.
I think you are going about it the right way. In spite of what I said above, immature and mature chickens often intermingle pretty well once they get used to each other. Some can be real brutes and bullies though, individual personalities come into play. My pullets normally make their way into the pecking order and stop this behavior about the time they start to lay so you may be close.
I’m not sure how you are managing the mornings when they wake up together, but I’d keep doing what you are doing. The pullet needs a predator proof place to sleep. Separating the aggressor is a good thing, don’t be too quick to put them back together as long as you can do that considering predators. A day or two isolation may affect her aggressiveness since it messes with the pecking order.
Introducing a lone chicken and her being a pullet both make it a bit more challenging, but with patience and some work you can do it. Good luck!