Sounds like your talking about fighting a bop in borg hunt. You can chase after them; all you have to do is switch your power settings to full power to engines and hit evasive maneuvers. You can try vming them if your in a sci ship or try target subsystem shields or engines.

The bird of prey is pretty much a hit and run ship. I think the bop pilot was just messing with you for fun. Out ranking someone doesn't mean you will automatically win. BO setup, equipment setup and skill come into play.