I've got an aggressive Calico that keeps chasing its original fish bowl mate (we recently upgraded to a 5.5 gallon aquarium)...it's squeezing it up against the glass and rocks and also seems to be chasing its tail..

Is this mating or bullying?

It might be either one. Goldfish like to chase each other; they don't need a reason. How big are the fish? Does the one doing the chasing have tubercles (white spots on the gill covers)? As long as they're not hurting each other, it should be ok. Sometimes goldfish get pretty aggressive with each other especially a male who wants to get eggs from a female. I hope they calm down for you!