Google bike uses a thumb joystick to control turning angle and reverse. I selected a simple
thumb joystick and
breakout board from sparkfun which looks identical to the kind found in ps2 controllers. The joystick contains two
potentiometers and a push button switch. At rest, the pots (potentiometers) are at their middle positions and will output half (2.5V) of VCC (5V), move the joystick and the outputs of the pots will move between VCC and ground. Pressing on the joystick closes the push button switch and causes the SEL output to go to ground. When the joystick is not pressed, SEL outputs VCC.
I laser cut a small bracket so the joystick could be temporarily mounted onto the handlebars using a rubberband. I've attached the svg file for the mounting bracket so you can modify it to your specific needs.