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In this paper, a novel optimization model is formulated to optimize the scheduling of battery swapping stations (BSS) operating electrified public bus transit fleets. The BSS consists of a number of battery modules that are combined together to create a MW-scale battery storage system. As such, the formulated optimization problem aims at minimizing the running costs of the BSS via i) exploiting the low electricity prices in the market (i.e., charging the battery modules at low prices), and ii) utilizing the BSS in the provision of grid ancillary services. The proposed model considers the operational requirements of the bus transit fleet to satisfy the energy needs of the battery electric buses (BEBs) and maintain their defined timetable. Also, the model integrates the power distribution network constraints such as bus voltages and line capacity limits to ensure its reliable operation. The impact of the BSS participation in the provision of ancillary grid services on the operation, degradation, and lifetime of the battery modules is investigated in this work by using a proposed saving cost index (SCI). It is demonstrated that the proposed model propels the economic viability of the BSS operation concept.