Just hit a straight road and start moving the bars, you will see how quick the bike will react. I did this when I first started just to see how it all worked.
You better watch Keith code again. Moving your body does nothing. You 100% must turn the bars in the opposite direction of turning. This is taught in every class I have been in. It's the only way to get the bike to turn. The bars shouldn't move from you moving your body, if they are your too stiff. You should be able to flap your arms like ringo aka chicken without the bars moving. Anyway you have to steer the bike.
You have to use the bars, you will not get a bike to turn any other way. Moving your body will get a small result but you must put input into the bars. If you don't know if you do, you better focus on this.