I do bodybuilding, or I bodybuild (less common for me)

I agree with Greg’s answer. “I do bodybuilding” is the best option. I think most native speakers would choose to avoid a construction with “do bodybuilding”however. For me personally, in British English, if someone asked me “What do you do for exercise/to keep fit?” I would avoid a “do” construction for bodybuilding and instead I would answer “I’m a bodybuilder”. This sounds the most natural of all the options. I can understand the confusion though- “bodybuilding” is an exception to the norm. For most if not all other sports and activities ending in -ing you will be able to say “I go”. For example “I go skiing” “I go rock climbing” “I go surfing”.

I'm a bodybuilder / I do bodybuilding.