The riddle
What Do You Call a Rabbit with Fleas?
Fleas, bugs and everyday speech
In everyday talk, "bug" means any small insect or crawling creature, and Merriam-Webster lists that sense of the word. A flea fits: Britannica describes fleas as small wingless insects that live on animals. The joke lives in the loose way people use the word. Scientists are stricter, and Britannica reserves "true bug" for the order Hemiptera, which includes cicadas and stink bugs. A flea belongs to another order, so a rabbit with fleas has insects but not, in the strict sense, bugs.
The rabbit in the answer
Bugs Bunny is a cartoon rabbit from Warner Bros. His first official cartoon, A Wild Hare, was released on July 27, 1940. The riddle names him only as the punch line, so no knowledge of his cartoons is needed beyond recognizing the name. A listener who has never heard of him will miss the joke, which is true of any riddle that ends in a name, and it helps to say "think of a cartoon rabbit" before asking.
A name as an answer
Many "what do you call" riddles end in an ordinary word. This one ends in a proper name, which changes the way it feels to tell. The listener has to produce a specific character, not a category. That makes it a short test of whether the group shares the same cartoons.
Keeping it light
Fleas are the only unwelcome detail, and the riddle needs nothing more about them. A rabbit with fleas is just a setup for the name. Tell it quickly, with the stress on "fleas", and move on to the next question.