Yes, they could spread the infection. With the stress of moving, that could make it all pop out, if the temp is quite cool, it may not show up for some time.
You can remove the infected bristlenose, and that may help minimise the parasites that eventually come from its body but even still there will still be parasites in the tank with the discus. Keep the temp up, increase aeration, keep up with the medicating and it will eventually run its course.