Is it possible to be Catholic and a bodybuilder?

The Church fully supports keeping healthy. But obsessing over any single aspect of ourselves neglects the rest, whether the obsession is work, status, control, eating or not eating. It is a matter of imbalance.

Bodybuilding is not a vocation; we exist for more than that. Your sense that it feels selfish shows you know something is off. Giving such attention to one's body makes a kind of god of it. If it were Christ's body you attended to, there would be no problem, because he is God. Consider how he related to us through his body: sacrificially, all the way, loving us with his body to the point of dying on the cross.

Eat well and keep up exercise for your health, but use your bodybuilding time for other things. Spend some reflecting on each suffering of his Passion and thanking him, preferably before the tabernacle, or else before a crucifix. That will not make you feel selfish; it will give your life balance and peace, because this is your vocation, and everything else will fall into place.