I think you would fall under jock since it goes by body type not necessarily activity:
Gay Men: Are You a Jock, Otter, Bear or Wolf?
I just put up my first article about the transgendered community. The Gym Rat Build. This is used to detect comment spam. Shemar Moore might be a good example of a gym bunny body. Considered sexually aggressive and part of the larger bear community.
I agree with commentors about Pups. Sporty gay lockerroom orgy with amateur jocks. Gym bunnies are native to both straight and gay worlds. Again, the primary difference is that gym bunnies care most about sculpting their bodies whereas gym rats are typically concerned with adding muscle size in hopes of becoming a bull. They are not necessarily part of the bear community and usually herd together as a bull might in its natural environment.