The electrification of large-scale bus depots will bring challenges for bus depot operators (BDOs) aiming to minimize operational costs. A potential solution for BDOs managing electric buses (EBs) with large batteries that are capable of vehicle-to-grid (V2G) operational functionalities, along with on-site generation facilities, is to actively participate in the energy market. This paper proposed a novel two-stage multi-objective stochastic optimization-based energy management system (EMS) for BDOs to trade energy in a day-ahead (DA) energy market while considering the expected cost of energy imbalances in the real-time (RT) market. The optimization model for charge–discharge scheduling is based on a mixed-integer linear programming approach. The uncertainties associated with the DA forecast are complemented by a stochastic model. Minimizing the cost of electricity and the penalty costs for battery capacity degradation are the objectives that need to be met simultaneously. The proposed EMS is evaluated using simulation studies considering a hypothetical bus depot in Australia. The effectiveness of the proposed EMS for overall financial savings is validated by comparing its performance with state-of-the-art scheduling strategies. Results show that the net energy cost for the proposed EMS is 38% lower compared to a deterministic scheduling strategy that does not allow V2G flexibilities, 33% lower compared to a deterministic scheduling strategy that allows V2G flexibilities and 17% lower compared to a stochastic scheduling strategy that minimizes overall costs.