Back when Bravo tried to create a spin-off of "Queer Eye for the Straight Guy," they did a massive publicity push for the new show "Queer Eye for the Straight Girl." As part of the publicity build-up, Bravo aired a special casting episode in which they documented their search for the new Fab-Five for the girl version. In the course of this special, Bob Harper can be seen auditioning for the fitness guru post for "QE for the Straight Girl." He didn't get the job, but the "Straight Girl" show fizzled pretty quickly. A year or so later, Bob had landed the "Biggest Loser" gig.
Given the above, I would lean towards "Bob is gay."
The jury's still out on Jillian.