Satellite clock bias (SCB) prediction is a crucial technology for satellite navigation systems, holding significant importance for Global Navigation Satellite System. This paper proposes a deep learning model for SCB prediction based on the fusion of the Beluga Whale Optimization (BWO), Convolutional Neural Network (CNN), Bidirectional Gated Recurrent Unit (BiGRU), and an attention mechanism. The CNN is utilized to extract the spatiotemporal characteristic information from the clock bias sequence, while the BiGRU fully extracts relevant features through forward and backward propagation. The introduction of an attention mechanism aims to preserve essential features within the clock bias sequence to enhance feature extraction by both CNN and BiGRU networks. Additionally, the BWO is employed to optimize parameter selection in order to improve model accuracy. Experimental verification demonstrates that for the BeiDou Navigation Satellite System's (BDS) hydrogen-maser atomic clocks, the predicted clock bias for 6 hours, 3 days, and 15 days are 0.078 ns, 0.475 ns, and 2.130 ns respectively - representing improvements of 31%, 45%, and 66% over CNN-BiGRU-Attention; 6%, 51%, and 56% over CNN-BiGRU; and 32%, 35%, and 73% over BiGRU, respectively.