This paper proposes a novel approach for investigating how energy storage devices (ESD) can affect a profit-maximizing distribution network aggregator’s bidding strategy in day-ahead (DA) electricity markets in the presence of uncertainties. The impacts of random renewable generation and demand on the aggregator’s real-time (RT) energy transactions and on network security parameters (e.g., line loadings and nodal voltages) are modelled using distributionally robust chance constraints (DRCC), which guarantee their validity with high probability as long as the true (but unknown) probability distribution of random variables belongs to an ambiguity set. This paper adopts a data-driven approach for defining the ambiguity set using the first and second order moments of random variables extracted from historical data. The aggregator’s overall profit maximization problem (incorporating ESDs and DRCCs) is reformulated into a convex, deterministic equivalent and solved using the MATLAB-based Disciplined Convex Programming software CVX. Results from simulations performed on an actual 11-kV distribution feeder show that the proposed bidding strategy enables the aggregator to achieve an efficient trade-off between profitability in the DA market and risk exposure in RT. Additionally, the results demonstrate the ability of ESDs to further increase the aggregator’s DA profits (through energy arbitrage) without exposing it to additional risks in RT. The impact of incorporating ESDs on distribution network security parameters is also investigated under different settings of the aggregator’s risk tolerance. Finally, some considerations on computational burden and optimisation model accuracy are presented.