When I drop a bouncy ball it bounces back up to me. What force causes it to bounce?

I do not think that there is a "force" that causes it to bounce. it's the rubber (or whatever material) makes up the ball.

Gravity pulls the ball down to the centre of the Earth but the ground resists the ball in the opposite direction. If there was no resistance the ball would phase through the ground. This is Newton's Second Law. However since the ball is made of rubber (just an assumption), the force of the floor resisting the ball is higher than the force of gravity, hence the ball then flies back up.