Electric buses (EBs) have the advantages of zero-emission and low energy consumption in operation. The electrification of urban buses is being vigorously promoted in many countries to reduce carbon emissions and promote the realization of the “Carbon peaking and Carbon neutrality” goals. However, due to financial constraints and the fact that fuel buses have not yet reached the end of life and bus companies usually replace fuel buses with EBs in batches, there are differences in the battery health degree and driving range of each bus on the line, which makes the optimization of the vehicle scheduling scheme more complicated. Considering the impact of battery differences in the state of health and time-of-use tariff, this paper proposed an optimized scheduling model for single-route, with the objective of minimizing average daily charging costs, EB acquisition costs, and battery loss costs. Then, the model was transformed into two sub-problems, the vehicle scheduling problem and the charging scheduling problem. In the outer layer, the vehicle scheduling problem was solved by the improved simulated annealing algorithm (ISAA), whose perturbation strategy is designed with the operating intensity differences among EBs. And Gurobi was employed to solve the charging scheduling problem in the inner layer. Finally, an actual EB route was taken as an example to verify the effectiveness of the method, and the method was compared with the simulated annealing algorithm in the perturbation strategy which does not consider differences in vehicle operating intensity. Results show that the ISAA can increase the convergence speed by 31.8% and achieve high-quality solutions in a short time. Moreover, the generated scheduling scheme can not only arrange EBs to be charged preferentially in the off-peak period of electricity prices but also reduce the EB fleet size.