Physics of shooting in a bike chase

Here's a fairly common scene in a lot of action movies: 

A hero (usually male) is riding a bike (a fancy one) very fast while being chased by bad people. These goons aren't just chasing him, but they are also firing bullets at him. Our hero ducks to dodge the bullet and miraculously dodges every bullet fired his way. 

There is a flaw in this picture: 

Even if we assume our hero has superhuman reflexes, it's still not possible to dodge bullets just by the sound of the gun.

Why?

Bullets travel faster than sound. Assuming our hero ducks instantaneously (no lag) after hearing the sound, it's still pointless as...

When the hero ducks to dodge the bullet after hearing the sound, that bullet has either already passed him or hit him before he heard them fire.

So a hero who knows Physics will just be thankful that the sound he heard hasn't already killed him.