If you look at greyhound popular destinations (SF, LA, Seattle), busing is already very popular, into those cities. It isn’t really a thing society does, rather Texan prisons will give releases inmates open bus tickets if they have no one picking them up, and they go to cities where they’ll survive.
I took a greyhound as a kid from Vicksburg to Seattle (along the southern then northern route, over 4 days), and got to witness this first hand.
Anyways, you just don’t survive being homeless in Great Falls Montana, so either you are dead or you first wind up in Spokane, then eventually in Seattle.