I don't think he is called that for any particular reason. His fellow politicians viewed him as a goofy dumb Cowboy so they called him "Bingo Bob." If he did earn that nickname in some fashion the writers have yet to reveal it.
The episode where he is first mentioned only make reference to the fact that he is perceived to be in the pocket of mining interests and is not particularly swift on the uptake. But no actual source of the "Bingo Bob" moniker.
It's Andrew Lloyd Webber week! Which means...Musicals! Simon is miserable, Paula looks like a real human being for the first time in forever, and for a second, I thought Randy was giving the finger to Ricky Minor and the band. THIS...Is American Idol.