A system nonlinear dynamic modeling and stability analysis method is proposed in this paper to revealing the lateral dynamic instability of air suspension bus under special driving conditions. A three degree of freedom dynamic model of the system considering the nonlinear mechanical characteristics of air spring and tire is established. In order to realize the stability analysis of complex high-dimensional dynamic system，the dimension of the system is reduced based on the central manifold theory firstly，and then the qualitative behavior of the reduced system is analyzed to determine the necessary and sufficient conditions for the system to meet the requirements of saddle node bifurcation. The bifurcation behavior of the system under four working conditions at the equilibrium point is analyzed in the phase plane，and the evolution law of lateral dynamic instability of the air suspension bus with the change of vehicle speed and front wheel angel under different road conditions is mastered. Finally，the system stability analysis results are verified based on the vehicle dynamics simulation. The results show that the analytical analysis results are consistent with the simulation analysis results，which proves that the nonlinear stability analysis method proposed in this paper is effective and practical.