This paper studies the energy trading among flexible demand response aggregators (DRAs) and a distribution company (Disco) with self-owned generators. Instead of the conventional non-cooperative game based approach, the trading problem is formulated as a bargaining based cooperative model, where Disco and DRAs collaboratively decide the amounts of energy trade and the associated payments. This cooperative interaction can be beneficial to both Disco and DRAs, by reducing the aggregated peak demand and increasing the potential cost savings. The increased benefits from cooperation are fairly allocated among these participants, based on the Nash bargaining theory. Compared with the non-cooperative game based approach, the proposed bargaining cooperative model can further improve the benefits of Disco and DRAs. Moreover, the bargaining outcome can maximize the social welfare of the system. Considering the privacy and autonomy issues of participants, we utilize a decentralized solution to solve the bargaining problem, with minimum information exchange. Numerical studies demonstrate the effectiveness of the bargaining-based cooperative framework, and also show the improvement of benefits of the system.