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.
Costanzo is actually 26, so he and his "mom" are actually only 5 years apart. Other than that, I liked the show. Seems like a pretty sweet apartment for an unemployed actor, but Friends had the same problem.