Bilateral contracts are important risk-hedging instruments constituting a major component in the portfolios held by many electric power market participants. However, bilateral contract negotiation is a complicated process as it involves risk management, strategic bargaining, and multi-market participation. This study analyzes a financial bilateral contract negotiation process between a generation company and a load-serving entity in a wholesale electric power market with congestion managed by locational marginal pricing. Nash bargaining theory is used to model a Pareto-efficient settlement point. The model predicts negotiation outcomes under various conditions and identifies circumstances in which the two parties might fail to reach an agreement. Both analysis and simulation are used to gain insight regarding how these negotiation outcomes systematically vary in response to changes in the participants' risk preferences and price biases.