Bart and Homer are "innocent" bad boys...who seem like they might be soothed with a hug. Some of the other shows and movies that were inspired by the Simpsons took a darker turn.
When someone bwaahaas on FR, I general interpret it as kind of a verbal "mooning" (and am not much charmed).
Wikipedia’s unsourced response was that it’s just a rendering of an evil laugh with various spellings. Think of the villain from the early silent movies and probably even earlier on stage - any victorious evil laugh, generally somewhat camp in tenor.