Compressibility correction methods to two-equation turbulence models have been used widely to account for the compressibility effects in turbulent high-speed flows. The present study aims at improving the accuracy of base pressure/drag predictions with the two-equation turbulence models. To this end, a simplified Ristorcelli’s compressibility correction is selected to perform computational analysis for base flows in conjunction with the k − ω SST turbulence model. The source terms arise in the ω equation when Ristorcelli’s correction model is applied to the k − ω turbulence model. Further improvement is sought by applying Bayesian optimization to determine a user-defined parameter in Ristorcelli’s correction model. Numerical analyses have been conducted for flows past axisymmetric bases and projectiles, and the validity of the optimized correction model is examined. The solutions with and without the optimized correction are presented and compared with the results of the standard k − ω SST turbulence model and the experimental data.