You may think it’s the handlebars that do the steering on a bike, but your body actually does the majority of the steering. If you turn by just moving your handlebars, you will make turns that are wide and clumsy. The tighter and smoother the turn, the more you have to lean.
Your job is to use small motions to steer the front wheel as little as possible to keep the bike directly under your center of gravity.
Source: League of American Bicyclists