New hens

Ideally they should have been kept seperate from the original girls for longer just in case any had an infection, however this information is obviously too late now  . The one you call the bully was probably just trying to establish the pecking order which is pretty normal. Did they come from the same breeder and was they raised together?
As you have already introduced one and hopefully she will be accepted quickly I would now introduce the other one sooner rather than later as introducing just one at a time can lead to more problems.