|If you dropped a bullet and at the same time, fired a bullet directly at the ground, wouldn't the bullet fired at the ground hit the ground first?
Sure it would. The fired bullet will only hit the ground at the same time as the dropped bullet if the fired bullet is shot exactly horizontally. If you fire the bullet at the ground, then it starts out with an enormous downward component to its velocity. The falling bullet doesn't have this initial downward component to its velocity and never catches up.