Bimbo trivia can also be the same questions she knows she should be asking, but are much easier because of how ditzy she's become, and perhaps some even change into overt requests for sex.
Also, to help bring flavor into the game, little scripts for Cheerilee for each question would be nice.
Here's an example of your first question, the Socrates one, expanded into a full script, as well as given a 'bimbo variant: