Load aggregators (LA) face the uncertainty of load and price when they participate in load curtailment bidding (LCB) in power market. A day ahead optimization model with the objective of minimizing the agency cost of LA is proposed. In this paper, the power purchase, LCB and the control of adjustable load are described as a mixed integer linear programming model. A bi-level programming model is used to deal with the uncertain load, so as to the historical scenario method to uncertain price combined with scenario reduction. Based on the data of Pennsylvania-New Jersey-Maryland (PJM) power market, the proposed strategy is analysed. The results show that the proposed strategy and scenario reduction method can reduce the aggregators' agency cost by more than 4% and risks by more than 10%, improve the performance rate by up to 17.8%, and provide bidding technical support for the LA under uncertain problems.