Under variable-speed conditions, bearing fault signals exhibit significant non-stationarity and low signal-to-noise ratio (SNR). Traditional sparse representation methods based on static dictionaries are typically designed for fixed-speed scenarios, making them poorly suited to adapt to speed-induced signal variations, which leads to a notable decline in fault feature extraction accuracy. To address this problem, this paper proposes a R-nyi entropy-driven adaptive structural dictionary learning algorithm (RE-ASDLA), aiming to enhance the adaptability and diagnostic accuracy of dictionary learning under non-stationary conditions. The method constructs an overcomplete structural dictionary with time-varying responsiveness, tailored to the transient impact patterns of bearing faults under variable speeds. It overcomes the limitations of conventional segment-based analysis and enables precise extraction of sparse transient features from strong noise backgrounds. During the dictionary update process, a joint optimization of reconstruction error and R-nyi entropy is performed to adaptively refine dictionary parameters, enhancing sensitivity to time-varying features and establishing a time-frequency-sparsity collaborative diagnostic framework. Experimental validation is carried out using two sets of linear and nonlinear variable-speed simulation signals, one publicly available Ottawa bearing dataset, and one set of real onboard measurements. The results demonstrate that RE-ASDLA effectively suppresses background noise and reconstructs variable-speed fault features with high accuracy, even under low-SNR conditions. It maintains robust performance across different speed profiles and significantly enhances the adaptability of dictionary learning for variable-speed scenarios. Compared with fast path optimization and time-reassigned synchrosqueezing transform methods, RE-ASDLA shows superior performance in terms of reconstruction accuracy, time-frequency concentration, and fault feature representation.