As a critical mechanical component, the operational integrity of rolling bearings is essential for equipment safety. However, under strong noise interference, the weak fault features in vibration signals are difficult to extract. To address this issue, a novel fault diagnosis method is proposed in this paper, which integrates an improved speed time-varying filtering empirical mode decomposition (ISTVF-EMD) with an adaptive sine–cosine optimization algorithm (A-SCA), enabling precise and efficient extraction of fault features. The core of the proposed method lies in improving the conventional time-varying filtering empirical mode decomposition (TVF-EMD) by setting a maximum decomposition layer limit, effectively addressing issues of excessive components and low computational efficiency during the decomposition of low signal-to-noise ratio (SNR) signals. Furthermore, a multi-characteristic frequency energy concentration centrality (MCFECC) index is employed as a fitness function to guide A-SCA in adaptively searching for the optimal bandwidth threshold and fitting order parameters of ISTVF-EMD, thereby extracting components with the most enriched fault information. Validated through simulation and multiple test bench cases, the results indicate that the proposed method can not only significantly enhance the fault characteristic frequencies and their harmonics in the envelope spectrum, successfully diagnosing outer race, inner race, and rolling element faults, but also, compared with the original method, ISTVF-EMD substantially reduces the computational time while ensuring or even improving the decomposition quality. The method presented in this paper provides an effective solution for achieving precise and adaptive fault diagnosis of rolling bearings under strong noise interference.