It’s funny to think that something as pedestrian as a character’s preferred mode of transportation could offer any inspiration or insight. Does it really matter if they ride their bike everywhere or drive a gigantic pick-up truck or refuse to go anywhere they can’t walk to?
It may seem insignificant, but the kind of transportation your character uses affects their independence (how much autonomy do they have to do what they need or want to do, when they need or want to do it?), and if all of your characters move about in the same way all the time, it’ll start feeling samey. That’s not even taking into account places in the world and eras in history when things like gender, race, and class dictate the modes of transportation used.
Knowing the modes of transportation used by your characters (the main ones, at the very least) helps bring order to the story world while also providing ample opportunity for writerly mischief, and goodness knows that's where half the fun is. ^_~