Nowadays, charging stations, hydrogen refueling stations, and natural gas refueling stations are being integrated into hybrid energy refueling stations (HERSs) to save investment costs and offer diverse refueling services altogether. This research proposes a risk-averse energy dispatch strategy for HERSs, incorporating bounded user rationality and operational uncertainties. A boundedly rational mixed user equilibrium model is proposed to capture the mobility of heterogeneous traffic flow, including electric vehicles (EVs), hydrogen fuel cell vehicles (HFCVs), and natural gas vehicles (NGVs), each with distinct refueling demands characterized by bounded decision-making rationality. A grid-connected HERS model integrated with carbon capture and storage and on-site renewable energy sources is designed to provide sustainable refueling services to EVs, HFCVs, and NGVs. Furthermore, an HERS operator aggregates multiple HERSs to participate in the day-ahead and real-time electricity markets. The optimal equipment operation and energy bidding strategies for the HERS operator are solved using a risk-averse approach based on conditional value-at-risk, addressing operational uncertainties from heterogeneous refueling demand, electricity markets, and renewable generation. Numerical results have validated the effectiveness of the proposed method in promoting net-zero emissions, securing economic benefits, and mitigating risks associated with operational uncertainties.