If it continues to bounce, shocks or struts are likely suspects. Take the car to a repair shop and have them put it on a lift for a more thorough inspection. Visually inspect suspension components and tires, carefully noting signs of wear. Uneven tire wear or cupping is a sure sign something is amiss. Look for oil leaking from shocks and struts.
Leaks mean they are losing oil and dampening ability.
Check shock absorber and control-arm bushings. In time, they dry-rot and can fall out. Look at upper strut-mount bushings. Also made of rubber, they re susceptible to dry rot. If cracked, replace them.