Two input beams at the same frequency excite the counter-propagating modes of a bidirectional ring cavity. These modes are coupled in the presence of a homogeneously broadened nonlinear medium and the optical device acts as two bistable switches whose characteristics can be mutually controlled. After a proper account of interference between the forward and backward waves, new features of optical bistability in a bidirectional ring cavity are discussed. It is found that when the intensity of one of the incident beams is held fixed in a critical range, the device switches on but never switches off as the intensity of the other beam is first increased and then decreased to zero.