The bearings in one or both rear wheels are causing noise while driving.
From the description provided, it appears that you are familiar with the sound of a bad wheel bearing. It can be difficult sometimes to determine if it is one or both wheel bearings are the culprits behind the issues your Mazda is experiencing. Often times having a bad tire can also duplicate the same noises as a bad wheel bearing. With a situation like this, I highly recommend enlisting the assistance of a certified mechanic to perform a test drive on your Mazda 3 to confirm the cause of the noise. They will also be able to make the necessary repairs as well to keep your Mazda running smoothly and quietly.