I am only going to integrate one hen of my existing flock to this new flock of four birds because she is the only want I want to add to this breeding group. Should I take one of the new hens and her and put them together first and let them be together for a few weeks to see if anything happens? Also should I go ahead and bathe, worm and dust for mites to where the mites and worms have a week or two to get out of their systems?
You could do that, sure, if you have a way to do so. Many folks use a "sacrifice bird" to check new ones for disease.
I would definitely worm and dust for lice/mites on all the new birds. Worming usually requires doing it, then re-worming two weeks later to get any that hatch from worm eggs in their systems, so it would be a two week proposition, at least.