The unpredictability of drilling pressure in bolt support systems has emerged as a significant constraint on support efficiency. Current research gaps exist in the field of machine learning for pre-drilling pressure prediction in bolt support and the selection method for key parameters (kernel function and historical points) in Gaussian processes. This study proposes a novel prediction method for bolt support drilling pressure, leveraging hybrid optimization algorithms to identify the key parameters in Gaussian process time series regression. Initially, the Gaussian process time series regression algorithm is modeled. Through data computation and simulation, it is observed that employing the Gaussian process time series algorithm for predicting the drilling pressure of bolt support results in substantial variation in the outcomes when different combinations of kernel functions and historical points are used. Therefore, it is essential to identify the optimal kernel function and the most suitable number of historical points before utilizing the Gaussian process time series algorithm for predicting drilling pressure. Subsequently, three hybrid optimization algorithms (GA-GPR, PSO-GPR, and ACA-GPR) are employed to iteratively optimize the two key parameters (kernel function and historical points) in Gaussian process time series regression. Among these, the PSO-GPR algorithm proves to be the most effective for identifying the kernel function and historical points of the key parameters in the Gaussian process time series algorithm when applied to the prediction of drilling pressure in bolt support. Remarkably, even with a small sample size and a limited number of iterations, PSO-GPR achieves 80% accuracy while reducing time consumption by 60%. Finally, a prediction system for drilling pressure in underground bolt support is established. The algorithm's generalization capability is verified through the prediction of actual drilling pressure. Thus, this study provides a robust and efficient method for predicting drilling pressure in bolt support systems, potentially enhancing support efficiency significantly.