Are you just trying to get fertile eggs? Moving the hens back and forth may cause enough stress that they stop laying for a while. They only need to be with him for a few days for him to breed them. I have heard that sometimes (not always) a hen can stay fertile for up to 3 weeks. However, you do run the risk that the stress will stop them for laying for that period of time. Also, consider that even a healthy chicken can spread disease. Whenever new birds come in they should be quarantined for 30 days. I wouldn't take your bird to the rooster. If you want fertile eggs, it would be better to just get your own rooster.
Of course, if you just want eggs and don't care if they are fertile, you don't need a rooster at all.