Being capable of aggregating multiple energy resources, the energy service company (ESCO) has been regarded as a promising alternative for improving power system flexibility and facilitating the consumption of renewable resources in the electricity market. Considering the uncertain variables in day-ahead (DA) market trading, an ESCO can hardly determine their accurate probability distribution functions. Traditional interval optimization methods are used to process these uncertain variables without specific probability distribution functions. However, the lower and upper bounds of the intervals may change due to extreme weather conditions and other emergent events. Hence, a dual interval optimization based trading strategy (DIOTS) for ESCO in a DA market with bilateral contracts (BCs) is proposed. First, we transfer the dual interval optimization model into a simple model consisting of several interval optimization models. Then, a pessimistic preference ordering method is applied to solve the derived model. Case studies illustrating an actual test system corroborate the validity and the robustness of the proposed model, and also reveal that ECSO is critical in improving power system flexibility and facilitating the ability of absorbing renewable resources.