Most current automated essay quality assessment systems treat score prediction and feedback generation as separate tasks, overlooking the fact that scores provide a quantitative evaluation of quality, while feedback offers a qualitative assessment. Both aspects reflect essay quality from different perspectives, and they are inherently consistent and can reinforce each other. In this paper, we propose a novel bidirectional reinforcement learning framework that effectively utilizes this consistency constraint to jointly optimize score prediction and feedback generation, ensuring mutual reinforcement and alignment between them. In this way, our model is hope to obtain a simultaneous accurate ratings and consistent text feedback. We conducted extensive experiments on publicly available datasets. The results demonstrate that our approach surpasses the current state-of-the-art models, enhancing both scoring accuracy and feedback quality.