Bearing vibration data are often contaminated with noise, which is detrimental to equipment fault diagnosis and predictive maintenance. Denoising bearing vibration data is crucial. Traditional denoising methods have certain limitations. For instance, when employing wavelet denoising, fixed basis functions may fail to perfectly match all signal structures, potentially compromising denoising accuracy. Similarly, when utilizing data-driven tight frame (DDTF) denoising, the learned basis, due to the lack of noise constraints, may incur a risk of overfitting. To optimize denoising performance in both scenarios, this paper proposes a method that combines wavelet transform and DDTF dictionary learning to extract noise based on a doubly sparse dictionary. The specific approach involves mutually cascading the wavelet transform and DDTF. After applying the wavelet transform to the noisy signal, multi-layer wavelet sparse coefficients are obtained. DDTF processing is then applied to each layer of wavelet sparse coefficients. Subsequent inverse transformation achieves noise suppression. This method integrates the structural constraint capability of wavelet decomposition with the learning capability of DDTF, thereby mitigating their respective limitations to some extent. The denoised data are fed into a residual network model, and training results confirm that the proposed method achieves the best classification performance. Experimental results from both data denoising and deep learning classification demonstrate that the proposed method exhibits superior denoising performance. Although the algorithm structure of this method is more complex compared to other approaches, it is meaningful in scenarios where high-precision denoising is required.