<p>A nonautonomous periodic discrete model is proposed to characterize the dynamics of <i>Wolbachia</i> spread in mosquito populations under period-2 environments, where the <i>Wolbachia</i> strain in the first environment is less competitive than the one in the second environment. By introducing the associated Poincaré map, the existence, exact number, and stability of periodic solutions and the long-term behavior of the discrete model are analyzed. Sufficient conditions are obtained to guarantee the bistable dynamics of the model: the model has exactly two periodic solutions, among which one is unstable, and the other is locally asymptotically stable. The origin, corresponding to the <i>Wolbachia</i> vanishment, of the model is locally asymptotically stable. Counting the exact number of periodic solutions of nonautonomous periodic discrete models is always challenging. In this paper, we provide three exclusive methods to prove the uniqueness of the periodic solutions, together with their stability analyses. Biologically, the unstable periodic solution serves as a threshold for <i>Wolbachia</i> invasion, and the stable periodic solution identifies where <i>Wolbachia</i> will be stabilized. Numerical simulations are provided to locate these two periodic solutions and analyze the parameter space to identify regions where periodic solutions emerge or disappear through bifurcations.</p>