Mid-to-long-term trading with curve is an effective way to realize the connection between the mid-to-long-term electricity market and the spot market. Since bilateral negotiation is one of the two ways of green power trading, how to determine the time-sharing electricity and the time-sharing trading price of mid-to-long-term bilateral negotiation transaction is an unavoidable issue in the study of mid-to-long-term with curve trading. This paper proposes a method for determining time-sharing power and trading price in the mid-to-long-term bilateral negotiation transaction based on distributional robust optimization (DRO) and Nash Bargaining Theory in view of the double uncertainties of new energy power generation output and customer load. Firstly, for the dual uncertainty of output and load, the ambiguity set of the distribution uncertainty of maximum deal power is constructed using a Wasserstein metric as the distance measurement. Secondly, a DRO-based time-sharing power determination model is constructed. Again, the time-sharing trading price determination model based on Nash bargaining theory is constructed based on the determination of time-sharing electricity and the total benefit of the community of interest. Finally, the proposed method is validated and analyzed through case study. The results show that the proposed method takes into account the uncertainty of both generation and user, and is able to effectively solve the time-sharing electricity and the time-sharing trading price of mid-to-long-term bilateral negotiation transaction determination problem.