Transfer learning (TL) and domain adaptation (DA) methods have been utilized in bearing prognostic and health management (PHM), but most of the current domain adaptation methods do not take into account the feature scale change of degraded features when aligning the feature distribution, and these methods are more suitable for the classification problem, which is more robust to the feature scale change. However, they perform poorly in regression problems. In addition, most of the remaining useful life (RUL) prediction methods require preprocessing such as statistical feature extraction on the signal, which makes the prediction process complicated. To solve the above problems, a domain adaptation method based on the representation subspace distance (RSD) is proposed for predicting the bearing RUL under different operating conditions. First, the proposed CNN Self-Attention LSTM network (CSALN) model is utilized to extract the deep features from the original signal, which overcomes the limitations of the CNN in extracting time series. Then, the representation subspace distance in the Riemannian geometry of the Grassmann manifold is proposed as a domain transfer loss to learn domain invariant features. The modified method can align the feature distribution of the source domain and the target domain without changing the feature scale. At the same time, the bases mismatch penalization (BMP) is introduced to avoid destroying the semantic information of the features in the process of domain alignment. Finally, the effectiveness of the proposed method is verified by experiments on four types of transfer tasks, and its superiority is also demonstrated by comparison with other advanced methods.