I like ebikes, but I lean towards the comments promoting plain ol bicycles as the optimal option. Simply put, a bicycle's only requirement is a reasonably-flat surface. If nature had provided roads, it's entirely possible for evolution to have devised wheeled creatures. For the same energy consumption, a human moves roughly four times faster or farther on a bicycle. That's a lot of advantage for zero extra energy.

But getting back to objective requirements, the other thing working in the bicycle's favor is the sheer number of them today: over one billion across the entire Earth, with around 100 million produced per year. If a world calamity happened right now and society collapsed, the estimated 60 million horses would become a luxury, not a utility, where 8 billion people vie for resources.

Obviously, much like a game of Catan, the horses and bicycles of the world are not evenly distributed. So if you're going to acquire something solely to put in the bunker for a doomsday scenario, I'd suggest not putting a horse in there; they won't like the dark.