Rolling bearings are important components in rotating machinery. Their operating conditions directly affect the safety and reliability of mechanical systems. To address the problems of large model size, high computational cost, and difficult deployment in existing deep learning-based bearing remaining useful life (RUL) prediction methods, this paper proposes a lightweight RUL prediction method based on knowledge distillation. The proposed method uses a “teacher-student” framework to transfer degradation-related knowledge from a complex teacher model to a compact student model. A dual-distillation strategy that combines soft-target distillation and feature correlation alignment is also introduced to improve the feature representation ability of the lightweight model. The method is evaluated on the XJTU-SY bearing dataset through comparative experiments and ablation experiments. Experimental results demonstrate that the proposed method effectively reduces model complexity while maintaining high prediction accuracy, making it suitable for lightweight industrial deployment.