I...I feel so dirty posting this, but Billy's preference was actually revealed in canon. One of the fan-favorite episodes, 'Power Ranger Punks', has Billy and Kimberly turned into bullies by Baboo's magic potion. As part of his new 'bad-boy' look, Billy wears his pants with his underwear hanging out.

Plaid blue boxers. No high-quality screencaps of this episode exist ( :( ), but you can check it out if you want. Upon being cured, the first thing Billy does is pull his pants back up. It's adorable.


Here is a crude screencap showing the outfit. (And for the record, I disagree with the secret. I'd hit it anytime ;) )