The basic mechanics of the bike are pretty simple --- it’s basically a triangle with wheels and a chain drive to propel it forward. No batteries or engines. It seems obvious in hindsight .... And that’s why most people guess the bike was invented a long time ago. Yet the ‘running machine,' a kind of early proto-bike, debuted around 1817.
For much more on the history of the bicycle, check out Jody Rosen's book: Two Wheels Good: The History and Mystery of the Bicycle.