You know how in an earlier time passengers used to get bored crossing the empty expense separating Pacific states from the rest of civilization (the first trains took a bit longer than ours) and they would shoot buffalo and passenger pigeons (a kind of bird) through the window? Uh, when did that stop allowing that? Frankly if you took out a rifle on a first world train now (even if their windows could open) you would scare a lot of people. Or did they only do that in private sleeping compartments? Or then again I know nothing about this time, who knows maybe once you got on the train at Omaha everyone open carried like the Wild West and your seatmate wouldn't be noticed if he suddenly decided to unholster his self-defense revolver and kill a bison.
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This occurred because there was essentially an active campaign to wipe out the great Bison ("Buffalo") herds that the plains Indians depended on to support their way of life (and thus their pushback against American settlement).
It would have come to an end during the 1880's, as by then there were only a few hundred Bison left. Sighting one from the rail lines would have been exceedingly unlikely.