Due to the bus characteristics of large quality, high center of gravity and narrow wheelbase, the research of its yaw stability control (YSC) system has become the focus in the field of vehicle system dynamics. However, the tire nonlinear mechanical properties and the effectiveness of the YSC control system are not considered carefully in the current research. In this paper, a novel adaptive nonsingular fast terminal sliding mode (ANFTSM) control scheme for YSC is proposed to improve the bus curve driving stability and safety on slippery roads. Firstly, the STI (Systems Technologies Inc.) tire model, which can effectively reflect the nonlinear coupling relationship between the tire longitudinal force and lateral force, is established based on experimental data and firstly adopted in the bus YSC system design. On this basis, a more accurate bus lateral dynamics model is built and a novel YSC strategy based on ANFTSM, which has the merits of fast transient response, finite time convergence and high robustness against uncertainties and external disturbances, is designed. Thirdly, to solve the optimal allocation problem of the tire forces, whose objective is to achieve the desired direct yaw moment through the effective distribution of the brake force of each tire, the robust least-squares allocation method is adopted. To verify the feasibility, effectiveness and practicality of the proposed bus YSC approach, the TruckSim-Simulink co-simulation results are finally provided. The co-simulation results show that the lateral stability of bus under special driving conditions has been significantly improved. This research proposes a more effective design method for bus YSC system based on a more accurate tire model.