to ask your question more scientifically change the word bounce to the word "Velocity", or "change in velocity" after impact. we know what velocity is (speed that has direction) and we know what impact is (the event to where colliding bodies exert relatively strong forces on each other over a relatively short amount of time). now to answer your question you have to know there are three types of collisions:
1) elastic: for small bodies, like molecules. (snooker balls have a nearly elastic collision)
2) inelastic: for larger bodies. like rubber balls or basketballs
3) plastic: when the two objects colliding stick together. like a bullet hitting a tree
now since you're studying balls, it'll be of the "inelastic" kind. in inelastic collisions momentum is conserved and not energy since part of the balls energy is turned into sound or heat or maybe even to deform the ball.
after that long explanation here is the answer to your question. the velocity after collision depends on:
1) the velocity of the ball before collision
2) the mass of the ball
3) the coefficient of restitution (bounciness : D)
the coefficient of restitution is a property of collision and not an object. it is calculated with the following formula:
CR =-v/u
v is the velocity of the object after impact
u is the velocity of the object before impact
this number is between 0 and 1, 0: when objects do not bounce at all and 1 when the ball bounces elastically (in simpler terms when no energy is lost after collision and the ball bounces to the same height as where it was dropped from)
speaking of height another way to find CR is to use the following formula:
CR = sqrt(h/H)
h is the bounce height
H is the drop height
hope this helped, good luck