With the development of deep reinforcement learning (DRL), much progress in various perfect and imperfect information games has been achieved. Among these games, DouDizhu, a popular card game in China, poses great challenges because of the imperfect information, large state and action space as well as the cooperation issue. In this paper, we put forward an AI system for this game, which adopts opponent modeling and coach-guided training to help agents make better decisions when playing cards. Besides, we take the bidding phase of DouDizhu into consideration, which is usually ignored by existing works, and train a bidding network using Monte-Carlo simulation. As a result, we achieve a full version of our AI system that is applicable to real-world competitions. We conduct extensive experiments to evaluate the effectiveness of the three techniques adopted in our method and demonstrate the superior performance of our AI over the state-of-the-art DouDizhu AI, i.e., DouZero. We upload our AI systems, one is bidding-free and the other is equipped with a bidding network, to Botzone platform and they both rank the first among over 400 and 250 AI programs on the two corresponding leaderboards, respectively. Our codes are available at https://github.com/submit-paper/Doudizhu_plus .