Never tried ghosts with a betta, but I did once have a 5 gallon with a betta and 5 to 7 amono shrimp. The betta kept them hiding all day long. If he got eye sight of one, a chase was instantly started.
However, I also found my boy was getting fin tears, even before the shrimp. No sharp edges I could find. I finally decided that the only thing that made any sense was that he must have occasionally gotten his tail too close to the filter intake and his fins must have suddenly covered most of the intake greatly increasing the speed of the water flow, and perhaps suctioning him to the filter for a moment before he could force his way away tearing his fin. I never saw this happen, and every time there was a new tear, it was spotted the next morning when I would come into work (he was in a 5 gallon bow front corner tank in my cube at work).