Originally Posted by makeinu

Although it may not be conscious, I find it very unlikely if you didn't steer by pulling or pushing the handlebars. There are two ways to steer a bike (depending on the conditions). One is to actually turn the handlebars and the other is to shift your weight (and since the hands are a weight bearing point, shifting your weight, subsequently involves pulling or pushing the handlebars).

Also, the reason why you don't steer in the opposite direction you lean when you use your hands to shift your balance on a bicycle is because you don't push perpendicular to the bars, but parallel to the bars and pushing parallel to the bars does not rotate the bars. Moreover, unlike steering by rotating the bars, pushing parallel to the bars to lean cannot be accomplished with just the palms of the hands because the only force holding your hand against the bar is the grip of your fingers. This is why just using a few fingers to grip the bars is not ideal (regardless of whether or not it is necessary...as so many have pointed out).