Overall the Car Ride is Very Bouncy Or Mushy

Weak shocks or weak strut cartridges.
Before explaining this, we'll need some background info on suspensions. A suspension system has two key components - shocks and springs. Sometimes these two components are separate from each other and sometimes they're integrated into a single unit called a "strut". The "shock" portion of a strut is often called a "strut cartridge".
In either case, the idea is the same - the spring absorbs the road's irregularities and the shock/strut cartridge keeps the spring from "bouncing" too much (i.e. it restricts the spring's contraction/expansion). Now then, as indicated in the problem, this car's ride is very bouncy/mushy. So, in light of the above explanation, this most likely means the shocks and/or strut cartridges are weak, right? Yes, because something is allowing the springs to "spring" too much and the above explanation implies that the shocks/strut cartridges are the culprit (i.e. by not restricting the movement of the spring).
What to do?
First, determine if this vehicle has shocks, struts, or both. A lot of vehicles have struts in the front and shocks in the rear. However, this may not be the case for this vehicle. Ask a local dealer's service department or check a manual covering the make/model in question. 
Next, try to determine if the bounce is mainly coming from the front or rear and, have the shocks or strut cartridges replaced only on that end. If the bounce still persists after having this work done, have the shocks or strut cartridges replaced on the opposite end as well. Most struts have replaceable cartridges. Therefore, it's often unnecessary to replace the entire strut. Ask a local dealer's service department if the struts on the vehicle in question have replaceable cartridges.