Semiconductor ring lasers display a variety of dynamical regimes originating from the nonlinear competition between the clockwise and counter-clockwise propagating modes. In particular, for large pumping the system has a bistable regime in which two stationary quasi-unidirectional counter-propagating modes coexist. Bistability is induced by cross-gain saturation of the two counter-propagating modes being stronger than the self-saturation and can be used for data storage when the semiconductor ring laser is addressed with an optical pulse. In this work we study the response time when an optical pulse is injected in order to make the system switch from one mode to the counter-propagating one. We also determine the optimal pulse energy to induce switching.