To explore effective mechanisms for new entities, such as electric vehicle (EV) aggregators, to participate in electricity markets under the “dual-carbon” goals, this paper proposes a multi-dimensional harmonious bidding strategy for EV aggregators in the energy-demand response market. First, at the day-ahead stage, EV clusters are classified based on the users’ travel characteristics, and their adjustable potential is assessed for participation in day-ahead energy market bidding. A corresponding day-ahead bidding model is established to evaluate market benefits. Second, the adjustable potential is updated in real-time through monitoring data. To avoid penalty for deviation, EV aggregators purchase both positive and negative bidding resources from demand response aggregators, i.e., re-biding through the demand response market. Then, to explore the multi-dimensional harmonious bidding strategy of EV aggregators, two price-setting models based on non-cooperative and cooperative game theory are considered and compared with the price-taker mode. Finally, case studies verify the effectiveness of the proposed strategy in improving economic benefits in the power market while contributing to peak shaving and valley filling in the grid.