I don't think it is a sport. Most of the formal definitions of "sport" have three requirements:
(1) Involves skill
(2) Physical exertion
(3) Competition
I would also add a #4, that success in #3 is improved by physical conditioning of the body. Anything that lacks any of the requirements is a borderline sport at best, and probably a game rather than a sport. These requirements are why things like football/baseball/soccer/basketball/track&field/volleyball/hockey/boxing/tennis are obviously sports, things like golf/bowling/autoracing are debatable, and things like billiards/darts/poker/beanbag toss are obviously games.
Bodybuilding only has #3 and #4 in my opinion. Posing is not physical exertion, and what are the involved skills exactly? It surely takes an extreme dedication to the training/eating/"supplements" lifestyle at the professional level, but I would not call that a skill. Anyone who wants to make the sacrifices involved can do so, although they may not have the genetic predisposition to become a pro. This is admittedly true of many other real sports, though (i.e. anyone can train like an NFL linebacker but very few will ever be able to become one).