With the rapid development of high-bit-depth display devices, bit-depth expansion (BDE) algorithms that extend low-bit-depth images to high-bit-depth images have received increasing attention. Due to the sensitivity of bit-depth distortions to tiny numerical changes in the least significant bits, the nuanced degradation differences in the training process may lead to varying degradation data distributions, causing the trained models to overfit specific types of degradations. This paper focuses on the problem of blind video BDE, proposing a degradation prediction and embedding framework, and designing a video BDE network based on a recurrent structure and dual-frame alignment fusion. Experimental results demonstrate that the proposed model can outperform some state-of-the-art (SOTA) models in terms of banding artifact removal and color correction, avoiding overfitting to specific degradations and obtaining better generalization ability across multiple datasets. https://github.com/duanpanjun/BVBDE