The uncertainties induced by electric vehicle (EV) demand and market operations pose huge challenges to the optimal bidding decision of the EV aggregator (EVA) in the day-ahead (DA) market. Note that a risk-neutral bidding solution with the expected cost minimization may make the EVA suffer a high financial loss in the market. As such, in this study, a risk-averse bidding strategy is developed to support the EVA to participate in the market via the conditional value-at-risk (CVaR) to handle market price volatility. Specifically, the strategy minimizes the CVaR metric over a collection of real-time (RT) clearing scenarios to reduce the energy transaction risk of the EVA in the market. Moreover, the model is reformulated as a linear programming (LP) problem that is mathematically tractable and can be efficiently solved. The proposed solution is extensively assessed through experiments based on the PJM market against the risk-neutral bidding strategy as a comparison benchmark. The numerical results reveal that the proposed risk-averse bidding strategy outperforms the risk-neutral one in terms of risk control, which enables the EVA to avoid suffering a huge financial loss incurred by RT clearing prices. In addition, the transformed LP model is superior to the original model in computational efficiency.