In the operation and management of Underground Gas Storage (UGS), the accurate and efficient calculation of bottom hole pressure is crucial for the dynamic analysis and production optimization of gas wells. To enhance the operational and maintenance efficiency of UGS, this paper innovatively proposes a new method for calculating bottom hole pressure. The study begins by comprehensively analyzing the key factors affecting bottom hole pressure calculation during gas injection, withdrawal, and shut-in stages based on the wellbore flow theory. Subsequently, it delves into the characteristic variables closely related to bottom hole pressure and constructs a neural network model on this basis. Finally, by integrating the wellbore flow equations under different well conditions, using theoretical models to generate samples, and establishing a loss function guided by real samples, a theory and data-driven neural network model (TDDNN) has been successfully developed, achieving rapid and accurate calculation of bottom hole pressure. The novel method significantly outperforms traditional techniques across five precision metrics, including Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), and an enhanced R-squared (R