With the advancement of Vehicle-to-Grid (V2G) technology, Electric Vehicle Aggregators (EVAs) can participate in the demand response electricity market by consolidating a large number of dispersed Electric Vehicles (EVs) to meet market entry thresholds. A bidding strategy for EVAs from a non-cooperative game theory perspective is proposed. In the framework, EVAs engage in multiple bidding rounds aiming to maximize their individual profits, while the power grid operator clears the market with the objective of minimizing dispatch costs. Based on the proposed bidding strategy and market clearing outcomes, day-ahead hourly charging and discharging compensation prices are formulated and announced. Finally, an optimal solution for the bidding strategy is obtained using an iterative best response method combined with a genetic algorithm. The case study demonstrates that the proposed method can effectively solve the bidding decision-making scheme in non-cooperative game scenarios involving multiple EVAs simultaneously.