The electrification of public transportation has picked up pace with the worldwide introduction of Battery Electric Buses (BEBs). In India, the BEB operations are now even expanding to hilly regions with extreme climatic and topographical conditions. In this study, we propose an energy consumption estimation model for BEBs operating in hilly regions. The study examined BEB operations on a few selected routes in the hilly terrain of the Leh district of Ladakh, India, to understand the important factors influencing their energy consumption. A hybrid data collection methodology was adopted by employing GPS, dash-board images and readings recorded from various on-board instruments like altimeters and temperature devices. Linear regression modeling was performed to determine the effects of terrain and other factors like passenger weight, ambient temperature, etc., on the energy consumption of the BEBs. We used the average gradients of the route segments between consecutive data readings for the modeling purpose. Results show that the predominant factors influencing the energy consumption of the BEBs are gradient and the passenger loading. BEB charging patterns were also assessed to estimate the expected time to charge various State of Charge (SoC) ranges of the battery. This study will help the stakeholders to critically design and make operational choices regarding BEB operation in the extreme geographical conditions like that of Leh.