The problem of H_∞ bumpless transfer control for networked switched systems with exogenous disturbance is investigated via an event?triggered mechanism. A novel method is first proposed to characterize the bumpless transfer performance at both switching instants and triggering instants, and an adaptive event?triggered mechanism dependent on the control bumps is designed to effectively suppress the sharp jumps in control signals resulting from the combined effects of subsystem switching and event-triggering. A dwell time-dependent and state?dependent hybrid switching law is developed. This strategy overcomes the limitations of conventional state?dependent switching laws by relaxing the non?increasing requirement of the Lyapunov function at switching points. Furthermore, by using the multiple Lyapunov function method, the sufficient conditions for the networked switched systems to be exponentially stabilizable with H∞ bumpless transfer performance are given, the H_∞ bumpless transfer controller is also designed. Finally, a numerical example is provided to demonstrate the validity and superiority of the results in this paper.