The classification of coal bursting liability (CBL) is essential for the mitigation and management of coal bursts in mining operations. This study establishes an index system for CBL classification, incorporating dynamic fracture duration (DT), elastic strain energy index (WET), bursting energy index (KE), and uniaxial compressive strength (RC). Utilizing a dataset comprising 127 CBL measurement groups, the impacts of various optimization algorithms were assessed, and two prominent machine learning techniques, namely the back propagation neural network (BPNN) and the support vector machine (SVM), were employed to develop twelve distinct models. The models’ efficacy was evaluated based on accuracy, F1-score, Kappa coefficient, and sensitivity analysis. Among these, the Levenberg–Marquardt back propagation neural network (LM-BPNN) model was identified as superior, achieving an accuracy of 96.85%, F1-score of 0.9113, and Kappa coefficient of 0.9417. Further validation in Wudong Coal Mine and Yvwu Coal Industry confirmed the model, achieving 100% accuracy. These findings underscore the LM-BPNN model’s potential as a viable tool for enhancing coal burst prevention strategies in coal mining sectors.