That doesn't sound particularly legal. Your gun bounces when you're on the move because it's supposed to. That's what vertical stabilizers are for ... to try to keep the gun on target better while moving.
The best way to keep your gun on target while on the move is to engage auto-aim. You won't be aiming at weak spots. OTOH, if you're trying to circle or strafe a target while on the move, you're probably trying to hit the enemy's sides or rear and your chances of penning auto-aimed shots aren't bad against soft targets. Of course, trying to get your gun on target that first time when you're moving can be difficult. So if you see your target before you start moving, consider engaging auto-aim at that point so that you're not tearing your hair out trying to get the reticule on target when it's bouncing all over the place when you're moving.