Well, one motor would control the drive wheel, and another something, mounted to the wheel, would control the tilt of the robot, doing the balancing. This way you don't have to worry about combining movement with balancing in the same control loop. However, you would need to be able to balance along 2 axis (Forward and back, and side to side).
However, I want you to think very carefully about this, as it is NOT a simple problem. Ever ride a unicycle? So, when it accelerates, inertia will tilt the body back, and same with deceleration. However, what happens when you want to turn? How do you even turn, you have only two directions of motion, forward and back. This means you need to Tilt the robot to turn sideways. Or the wheel needs to turn (which given its reference, the robot would actually turn, not the wheel).
Now you have to balance while either 1) The robot is tilting or 2) while the wheel rotates around, and now the axis of movement has shifted changing the balance..
I'm pretty sure that this is on the level of PhD or Post-Doc research. Assuming parts even exist. If you could build a working prototype in your garage, I imagine people will have jobs for you. Good luck!