I was backing out of my driveway and rubbed my bumper on the side of my sons white car. Is the any way to rub this paint off?

Depending upon the situation, a paste wax and cheese cloth may get some of it off.

You can use fibreglass rubbing compound very gently with a soft cloth. I have used Softscrub to remove paint marks on my car, or even baking soda will work. Any gentle abrasive.