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Many deep learning methods typically assume that the marginal probability distribution between the training and testing bearing data is similar or the same. However, the probability distribution of rolling bearings may deviate significantly under diverse working conditions. To address the above limitations, a novel transferable remaining useful life (RUL) prediction method integrated with Bayesian deep learning and unsupervised domain adaptation (DA) is proposed. First, the signal alignment is executed on the data after the first prediction time to maintain the same granularity and scale across both source and target domains. Second, the multi‐domain features are extracted and sent into the dual‐channel Transformer network (DCTN) incorporating the convolutional block attention module (CBAM) to adequately exploit the abundant degradation information. Then, the DA module is incorporated into the model to mitigate the distribution discrepancies of the extracted high‐level merged features between the source and target domains. Finally, by applying the variational inference method, the DCTN‐CBAM is extended to the Bayesian deep neural network, and the RUL prediction and its corresponding confidence intervals can be conveniently derived. In addition, the generalization capability and effectiveness are validated through six bidirectional transfer RUL prediction tasks across two rolling bearing datasets. The experimental results demonstrate that it could provide a more reliable RUL prediction and efficiently account for the prediction uncertainty. [ABSTRACT FROM AUTHOR]