The surprising thing is that it is way more than "a few feet". Apologies for repeating myself, but watch https://www.youtube.com/watch?v=oZAc5t2lkvo (And that is not on smooth terrain)

And nitpick: typical bicycles aren't symmetric left-right. The chain and gears make them heavier at the right. Most mass is close to the center line, though, so its moment is negligible, especially when ridden by a human.