When your car bounces when you stop it's likely caused by bad shocks or bad struts.
If your vehicle shakes or vibrates when you are stopped at a stoplight or stop sign then it could be bad motor mounts.
However for a car bouncing when you stop the suspension is likely bad or your shocks are bad.
Most cars have struts on the front and rear and when those struts wear out they can cause the car to bounce when stopped and bounce when you go over bumpy roads.
If you can push down the car on the front or back easily and it bounces back and forth then it likely is the struts or shocks going bad.
It would be best to have the struts or shocks replaced because not only is it uncomfortable to ride in a bouncy car it can also be dangerous and wear your tires out faster as well.