I have tried tons and tons of combinations. After hours of experimentation I have found that carrier bays do nothing. You can't make a carrier in this game. No combination of orders that I have found do anything. Fighters will never return to a ship for repairs no matter what. I have seen fighters that have retreated from damage just fly around uselessly and badly damaged near a cruiser with a carrier bay and it will never go in.
Just a heads up for anyone else trying to make this work. Do not bother.