For large-scale implementation of battery-electric buses (BEBs) in Indian cities, careful optimization of charging scheduling under time-of-day (ToD) tariffs, transformer and feeder capacity constraints, and battery health considerations is required. This study presents a mixed-integer linear programming (MILP) model that integrates energy prices, peak demand penalties, and battery degradation costs to minimize daily operating costs by jointly scheduling charging sessions across multiple depots. A case study based on the MTC context of Chennai city, using synthetically generated but field-aligned fleet and infrastructure data, is used. Considering Vyasarpadi and Perumbakkam depots, two scheduling strategies were evaluated: a baseline parallel charging strategy and a staggered peak-shaving strategy. Specifically, the staggered strategy reduced peak demand from 360 kW to 20.46 kW, resulting in a total daily operating cost savings of approximately ₹ 101,000 for a depot. Especially, this reduction is achieved without compromising the State of Charge (SoC) potential or incurring increased battery degradation costs. The proposed approach demonstrates that it is possible to deliver significant cost savings through a staggered strategy while maintaining operational readiness.