The bearings, being one of the most easily damaged critical components, often have early fault that are masked by noise. Therefore, efficient feature extraction from bearing signals is crucial. This paper introduces Tensor Singular Value Decomposition (TSVD) technology and proposes a bearing fault feature extraction method based on three-dimensional tensor modeling and adaptive r-term approximation. This method first constructs a tensor from the collected data. Then, it performs a Fourier transform on the tensor to convert it into the frequency domain. After that, an economical singular value decomposition (SVD) is carried out on each slice in the frequency domain. During this process, the number of retained components, denoted as r, is dynamically determined based on the proportion of singular value energy, achieving a sparse representation of the signal. Compared to the traditional matrix SVD method, TSVD makes full use of the multi-dimensional structure of the tensor and performs better in separating features of different fault types, such as the inner and outer rings of the bearing. Additionally, the adaptive r-value selection strategy strikes a good balance between decomposition accuracy and computational efficiency, providing a new solution for the online monitoring and fault diagnosis of rotating machinery.