To address the issues of traditional forward design for structural colors, such as limited optimization parameters, time-consuming computations, and non-tunable static structural colors, an inverse design method for structural colors of metasurfaces based on the Bayesian optimization algorithm is proposed. By introducing tunable phase-change materials to design nanoantennas and combining the Bayesian optimization algorithm with the finite-difference time-domain method, the structural color parameters of the metasurface are simulated and optimized. The designed structure utilizes Mie resonances in reflection mode to generate structural colors, while reversible color tuning is achieved through phase transitions of the phase-change material. Simulation results demonstrate that the proposed structural color device exhibits dynamic tunability of metasurface colors, with color differences of 63.30, 69.30, and 54.21 achieved at wavelengths of 450 nm, 545 nm, and 660 nm, respectively, along with angle-sensitive characteristics.