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 think by the time Season 4 comes about, I may have worked out in my mind exactly what was going on in the last three minutes or so. If Peter never existed, then surely none of the events which caused the war between universes would have occurred?