In our house we call this "the lip". Both our dogs occasionally do it to each other. It is a warning that means "stop it"...stop sniffing my foot, stop playing with that toy, I want it. Part of this is a way for the dogs to work out their relationship with each other. Like kids, it is hard to figure out when to intervene, and to give advice without being there is a little risky. But what I do when I feel one of my dogs is being unreasonably testy is admonish that dog in a tone of voice that shows I am not going to tolerate that. "Hannah, I don't want to see any lip out of you!" "No LIP!"
Your dogs are still in an period of working out who is what in terms of status. Obviously Bailey wants to be top dog and there is nothing wrong with that, but it doesn't mean that she should be allowed to take advantage of him. If it is of any comfort to you, Hannah and Tucker had what seemed like was going to be a tendency to get into fights in the beginning. I actually had to pull them apart several times. But over the weeks the tendency decreased and then eventually completely disappeared. Now they are inseparable. Remember Bailey has been through a lot. She sounds like a wonderful dog. Give her a chance to learn the ropes of getting along with PJ and living in a new household. You have to help her learn.