The conventional bus propagation process has two main shortcomings: one is bus bunching, the other is extra energy consumption by idling at signalized intersection and unexpected speed variation along the route. To overcome these problems simultaneously, an extended bus propagation model and an anti-bunching control are proposed. To extend the time-based bus propagation model, we employ finite state machine and intelligent driver model to establish a spatial-temporal based bus propagation model accounting for bus dynamic motion and passenger swapping behavior between bunching buses. To mitigate bus bunching and improve bus fuel economy in a cyber-traffic environment, an anticipated average speed planning is employed to improve headway regularity and reduce the chance of encountering red light, and then model predictive control accounting for state and control constraints is used to generate a smooth speed trajectory for connected bus to follow the commands given by anticipated average speed planning, which will in turn ensure that all the connected buses traverse signalized intersection and approach downstream stop in ecological driving behaviors. Numerical simulations show that the proposed model can imitate passenger swapping behavior when bus bunching occurs, and the anti-bunching control is suitable to mitigate bus bunching and guide connected bus to traverse signalized intersection and reach downstream stop with fewer delays.