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In recent years, the microgrid system (MGS) has become an important method for the consumption of renewable energy sources (RES). In the actual operation process, the uncertainties of RES add to the complexity of the MGS operation. Furthermore, the MGS is often operated by multiple subsystem operators. The benefit distribution among subsystem operators is an important factor affecting the overall stable operation of the MGS. In order to resist the interference of the above factors, a two-stage optimization method is proposed in this paper, which includes a bi-level robust optimization (BRO) model in the overall scheduling stage of the MGS and a nucleolus-based cooperative game (NCG) model in the internal cost allocation stage among the subsystem operators. The simulations demonstrated the following outcomes: (1) the P2G device can reduce the operating cost of the MGS by converting electricity into natural gas when the electricity price is low; (2) the two-stage optimization method can ensure the stable operation of the MGS by resisting the disturbance of uncertain wind power outputs in the overall scheduling stage and realizing a reasonable cost allocation among the subsystem operators in the internal cost allocation stage.