Featured Application: By giving specific road excitation, the differential equations and analytical solutions derived in this paper can be used to quickly estimate the vertical displacement and acceleration of the bus passing through this section of the road. The theoretical results and formulae in this paper can provide some guidelines for bus design and bus driving.The comfort of a bus running on different road conditions is a matter of public concern. In this paper, the differential equations of motion are established for a bus running on different road conditions and the whole driving process is mechanically analyzed. Firstly, the bump degree at different positions is quantitatively analyzed and it is found that the rear row is bumpier on different roads. Then, the relationship between the speed of the bus and the vertical displacement and acceleration is quantitatively described. Regardless of the speed, a similar displacement and acceleration will be eventually achieved, but the speed is higher, and the duration of maximum displacement and acceleration is longer. When the speed is 8 m/s, resonance occurs on the bus during road condition II. Finally, the change in vertical displacement and acceleration under the action of different spring stiffness coefficient ratios of the front and rear wheels is quantitatively analyzed. High stiffness ratios mean less displacement and acceleration. By establishing an actual excitation road surface, the differential equations and analytical solutions in this paper can be used to roughly analyze the mechanical response of a traveling bus. These results can provide some guidance for the design and driving of buses.