We investigate optical bistability (OB) behavior in an asymmetric three-coupled quantum well structure inside a unidirectional ring cavity. By controlling the assisting coherent driven field and the frequency detunings of the two control laser fields, we find that the appearance and disappearance of OB can easily be controlled by adjusting the positions of the dual electromagnetically induced transparency windows. Analysis in the dressed-state picture is also given. Our scheme may be used for building more efficient all-optical switches and logic-gate devices for optical computing and quantum information processing.