Are there potentiometers that are built so that they snap back after the person lets go, or is that something I'm going to have to make on my own?
This would probably be something you would have to build.
Motorized potentiometers have already been mentioned, but what you are describing sounds more like a spring return system; maybe a pre-tensioned coil spring around the pot's shaft might work? Or a tension spring with a cord of some sort wound on the pot's shaft?
At any rate, this is similar to how some hobby RC transmitter joysticks, as well as some older computer joysticks (as well as current thumbsticks) are setup, except they are designed to "return-to-center". Something to keep in mind, should you pursue this mechanism, is that your initial beginning value may not be the same as the later values when the pot is returned back to the beginning by the spring. You will need to take care of this in software, or some other fashion, most likely. Back in the earlier PC days, you had to go thru a "calibration" routine with joystick games to set the proper max/min positions and center of the joystick so it would work properly with the games.