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.
I just find him rather annoying now. I don't dislike him for winning, but his method of play just leaves a lot to be desired. I think it's just that many of us are traditionalists who grew up watching Jeopardy and saw people do the top-to-bottom style.