Okay, major ProTip here:
One thing that really helps to stay balanced is to slide forward out of the saddle as you come to a stop so you are straddling the top tube (but not actually sitting on it) put most of your weight on whichever pedal is currently pointed down;
this lowers your center of gravity ever so slightly, and also allows one foot to reach the ground.
That extra foot on the ground in addition to the two tires makes keeping the bike from falling over really easy without having to make any corrective motions at all, been totally motionless all through a 2 min traffic light!
With this technique I can stay balanced one handed; or even do tricks like drinking from a water bottle (on the bike!) and using hand signals.