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.
This looks weird/intriguing in the commericals. Season Passing-ing. Yea, they brought it back on April 1st as a gag and, just six weeks later, they already have a plan to bring it back and new footage. A Christmas miracle!