Inaccuracy of buses is a common situation. A common practice is that a certain amount of slack is usually added to the schedule of bus operation, so that the bus can execute the schedule in most cases. On the other hand, slack means that buses sometimes have to wait for a while at the station or slow down while driving. Since the bus cannot accelerate the driving process by itself, this method cannot make the bus fully implement the schedule. Researchers invented the Transit signal priority (TSP) and conditional signal priority (CSP), the purpose of which is to give the bus signal priority to speed up when it is delayed to a certain extent. Some previous work has studied the driving process of buses with CSP. However, there is still room for further improvement in the mathematical description of the bus driving process based on CSP. In this article, we analyze the driving state of the bus under different CSP states, that is, positive and negative. Then a series of representative and operational assumptions are given. These assumptions can be used as the basis for future research on such topics. With the assumptions, we give a mathematical model of the bus driving process using CSP. According to some performance indicators of the bus driving process obtained in the modeling process, an optimization goal is established to comprehensively improve the driving effect of the bus. Mathematical analysis and numerical solution verify the applicability of the model.