A city bus carries a large number of passengers, and any traffic accidents can lead to severe casualties and property losses. Hence, predicting the likelihood of accidents among bus drivers is paramount. This paper considered occupational driving characteristics such as cumulative driving duration, station entry and exit features, and peak driving times, and categorical boosting (CatBoost) was used to construct an accident probability prediction model. Its effectiveness was confirmed by the daily management data of a Chongqing bus company in June. For data processing, Multiple Imputation by Chained Equations for Random Forests (MICEForest) was used for data filling. In terms of prediction, a comparative analysis of four boosted trees revealed that CatBoost exhibited superior performance. To analyze the critical factors affecting the probability of bus driver accidents, SHapley Additive exPlanations (SHAP) was applied to visualize and interpret the results. In addition to the significant effects of age, rainfall, and azimuthal change, etc., we innovatively discovered that the proportion of driving duration during peak duration, the dispersion when entering and exiting stations, the proportion of driving duration within a week, and the accumulated driving duration of the previous week also had varying degrees of impact on accident probability. Our research and findings provide a new idea of accident prediction for professional drivers and direct theoretical support for the accident risk management of bus drivers.