Who discovered the modern bicycle?

Answer 1

They were originally called the safety bicycle.

Answer 2

First the bike didn't have any drive, you kicked yourself along with your feet on the ground.
Then someone put a pair of pedals on the front wheel.
After that the front wheel got bigger to get the speed up.
Then someone invented the chain and sprocket, which allowed the drive to move to the rear wheel and the front wheel to shrink to a more regular size. As a bonus thes bikes didn't flip over as easy during braking.
After that we've pretty much reached the modern bikes. Changes like multiple gears and suspension have been successful, but in principle smaller than the ones listed above.

Answer 3

Discovered basically means "finding something that already exists", which doesn't fit the bicycle. John Kemp Starley is by many considered to be the inventor of the "modern" bicycle.