Mid-to-long-term trading with curve is recognized as an effective means to realize the connection between the mid-to-long-term electricity market and the spot market. Since bilateral negotiation is one of the two methods for green power trading, the determination of time-sharing electricity and the time-sharing trading price of mid-to-long-term bilateral negotiation transaction is an issue that must be addressed in the study of mid-to-long-term with curve trading. A method based on distributionally robust optimization (DRO) and Nash bargaining theory was proposed to determine the time-sharing power and trading price in the mid-to-long-term bilateral negotiation transaction, considering the dual uncertainties of renewable energy power generation output and customer load. Firstly, an ambiguity set for the maximum deal power distribution uncertainty was constructed based on the Wasserstein distance to address the uncertainties of power output and loads. Secondly, a quantity determination model based on distributional rubust optimization was developed. Following this, a price determination model based on Nash bargaining theory was established, taking into account the determination of time-sharing electricity and the total benefit of the community of interest. Finally, the proposed method was verified and analyzed through a case study. The results indicated that the proposed method effectively addressed the issue of determining the time-sharing power and trading price in mid-to-long-term bilateral negotiations by considering the dual uncertainties of power output and loads.