Bi-directional electricity trading of demand response (DR) and transactive energy (TE) frameworks allows the traditionally passive end-users of electricity to play an active role in the local power balance of the grid. Appropriate building energy management systems (BEMSs), coupled with an optimized bidding strategy, can provide significant cost savings for prosumers (consumers with on-site power generation and/or storage facility) when they participate in such bi-directional trading. This paper presents a BEMS with an optimization-based scheduling and bidding strategy for small-scale residential prosumers to determine optimal day-ahead energy-quantity bids considering the expected cost of real-time imbalance trading under uncertainty. The proposed scheduling and bidding strategy is formulated as a stochastic bi-level minimization problem that determines the day-ahead energy-quantity bids by minimizing the energy cost in the upper level considering expected cost of uncertainty, whereas a number of lower-level sub-problems ensure optimal operation of building loads and distributed energy resources (DERs) for comfort reservation, minimization of consumers’ inconveniences and degradation of residential storage units. A modified decomposition method is used to reformulate the nonlinear bi-level problem as a mixed-integer linear programming (MILP) problem and solved using ‘of the shelf’ commercial software. The effectiveness of the proposed BEMS model is verified via case studies for a residential prosumer in Sydney, Australia with real measurement data for building energy demand. The efficacy of the proposed method for overall financial savings is also validated by comparing its performance with state-of-the-art day-ahead scheduling strategies. Case studies indicate that the proposed method can provide up to 51% and 22% cost savings compared to inflexible non-optimal scheduling strategies and deterministic optimization-based methods respectively. Results also indicate that the proposed method offers better economic performance than standard cost minimization models and multi-objective methods for simultaneous minimization of energy cost and user inconveniences.