The Peloton Bike is designed to give you a great workout and ensure that you work as hard as you would in a live indoor cycling class. Because of this, there is not currently an option to pause your ride.
If you need to leave a class temporarily, or if you prefer to try a different one, simply tap the exit button on the top-left of the touchscreen. You can always delete the results of the class you exited if you don’t want to keep it in your workout history.