When I am traveling, I hitch-hike and train-hop. When I am in town (either Moab or Portland), I walk a lot and ride a bicycle. There is usually a spare bike around that somebody is willing to give me or lend me. I can find perfectly good bicycle tubes & tires in dumpsters, and often tools & parts in random places like sides of roads. I'm often astonished how things come when & where needed.
In the summer of 2007, I bicycled from Portland to western Wyoming with friends on an abandoned bike, then headed back by myself to Portland partway on the bike and train-hopped the rest of the way with the bike. Right after that I bicycled to Seattle from Portland, then all the way down to Sacramento, California, part-way with a friend. We never had to ask for tubes, tires, spare spokes, or tools, but either found all those things on the sides of roads, in dumpsters, or people offered things to us without us asking. It astounded me, because previously I had convinced myself that faith wouldn't really work with a bicycle.