The traditional cell transmission model (CTM), a well-known dynamic traffic simulation method, does not cater to the presence of moving bottlenecks, which may be caused by buses traveling within a network. This may affect the dynamics of congestion that is present and may also affect route choice by all vehicles on a network. The main contribution of this paper is to provide an analytical formulation for a mixed traffic system that includes cars and buses, which realistically replicates moving bottlenecks. We modify the CTM model using methods from the lagged CTM to recognize speed differentials between the free-flow speed of buses and cars. In addition, the impact of capacity reduction caused by buses was incorporated. These developments led to the replication of moving bottlenecks caused by buses within the CTM framework. The formulated variant of CTM was utilized to determine a system optimal assignment that minimizes the total passenger travel time across cars and buses. The proposed modified CTM model, defined as the BUS-CTM, has been applied on a road link and a more detailed network to demonstrate the effectiveness of the approach. The numerical results and the depiction of the bottleneck phenomenon within the model suggests that the BUS-CTM obtains more realistic results compared with the application of the traditional CTM in a mixed car-bus transportation system. The sensitivity analysis shows that bus passenger demand, passenger occupancy of bus, and bus free-flow speeds are the key parameters that influence the system performance.