A bus-involved crash unavoidably affects many passengers, causing severe consequences. Nonetheless, few studies have been comprehensively conducted to analyze the bus-crash severity. Accordingly, using the data of the bus crashes that have occurred in the UK in 2017–2019, this study constructs an extended hierarchical ordered probit model with heteroscedasticity (HHOPIT) to investigate the factors influencing bus-crash severity levels. Using AIC and BIC indicators, we confirm that considering the impact of variable heterogeneity on the threshold and error term is essential for interpreting bus-crash severity. Particularly, the frontal-impact-crash, wet-road, and moderate-speed-limit variables produce heteroscedasticity and significantly affect the crash severity level. Additionally, overturned-crash, multi-vehicle-crash, and morning-crash variables induce threshold variability. Based on the marginal effect of variables, it is confirmed that road-section, frontal-impact-crash, wet-road, junction-exit, and main-way variables increase the likelihood of severe injuries. Furthermore, the probability of slight injuries as consequences, increases with the influence of lower-speed-limit, roundabout, urban-crash, parking-crash, and moderate-speed-limit variables. This study additionally determines the factors that have inconsistent effects on the consequence of bus and passenger-car crashes. To improve the safety of bus services, the authorities must carefully consider the heterogeneity and specificities of the factors affecting bus-crash severity and appropriately formulate targeted policies.