In this paper, a novel adaptive nonsingular fast terminal sliding mode (ANFTSM) control scheme for yaw stability control (YSC) is proposed to improve the bus curve driving stability and safety on slippery roads. There are three major contributions in the design process of the bus YSC system. The first contribution is that the STI (Systems Technologies Inc.) tire model, which can effectively reflect the 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. The second contribution is 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. The third contribution is that the robust least-squares allocation method is used 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. To verify the feasibility, effectiveness and practicality of the proposed bus YSC approach, the TruckSim-Simulink co-simulation results are finally provided.