If a motorcyclist experiences a wobble while riding, they should close the throttle gradually and move to the shoulder. Gradually releasing the throttle will naturally decelerate the motorcycle, helping to stabilize it. A sudden stop or aggressive maneuvers can exacerbate the wobble, so it's crucial to glide to a safe stop at the side of the road where any necessary adjustments or repairs can be made. This approach allows the rider to manage the instability without losing further control, minimizing risk to themselves and others on the road.