Speaking as a former competitive ballroom dancer, I'm afraid that Bill Nye isn't very good. His technique is terrible, footwork sloppy, and his steps are much too big for cha cha. It looks like he's an ok social dancer and he knows how to lead, but that doesn't necessarily translate to competition, especially for something like cha cha, which requires snap and precision. In social swing, you can be pretty loose, and he's clearly used to that and hasn't figured out the control that cha cha requires.
It'll be interesting to see if he does any better at the Standard dances - waltz, tango, foxtrot, quickstep, and Viennese.
Also, he was creepy at his partner in the opening segments, with that "sexual tension and evolution" comment. Ick.