The most common reason that a car squeaks when you go over bumps is due to a worn or bad ball joint.
The squeaking sounds of a car when it goes over bumps is caused by the connecting ball joint or rubber bushing being worn out.
The ball joints on a vehicle are a connection that is where a metal ball is trapped inside in a cup lubricated with grease.
Sometimes the bushings get worn out and the grease is gone causing the squeaking.
Some ball joints can be greased but some ball joints are not able to be greased.
If you need new ball joints it can cost between $300.00 to $1,000.00 to replace the sets of ball joints depending on the vehicle.
If you can do it yourself then it will be cheaper.
Other causes of a car squeaking when going over bumps is worn out struts, worn out shocks etc.
You could try pushing down on the back or front of your car when it's sitting and see if you hear squeaking then and that can lead you to finding the problem.