The popularization of bridge employment is conducive to the realization of active aging, which requires not only the subjective initiative of retirees but also the active cooperation of local governments and relevant enterprises. This study combined evolutionary game theory with system dynamics to model and simulate the behavior of local government and enterprises on bridge employment, aiming to highlight the importance of government behavior and enterprise actions in the process of active aging and to analyze the effectiveness of different incentive and punishment mechanisms in promoting bridge employment. Results show that the system with dynamic incentive and punishment is easier to keep stable than the system with static incentive and punishment; specifically, the dynamic mechanism with low incentive intensity and high punishment intensity is better than other mechanisms. Finally, this study emphasized the importance of government policy to bridge employment and put forward relevant management implications.