The large amount of data collection in rolling bearing health monitoring brings about high data transmission pressure and high storage costs. To address the above issues, this paper proposes a data collection and reconstruction method based on compressive sensing. This method directly collects compressed data and accurately restores the original signal based on a small amount of data, reducing the collection of redundant information and free up data storage space. Due to the fixed gradient step size in the reconstruction process of vibration signals using traditional iterative shrinkage threshold algorithms (ISTA), an improved ISTA (IISTA) is proposed to address issues such as slow convergence speed and low reconstruction accuracy. Firstly, an acceleration operator considering variable step size is proposed to estimate gradients, which can accelerate the process convergence speed. Then, in order to break the limitation of fixed internal gradient step size, the bidirectional search principle is introduced to backtrack, and the iteration step size changes adaptively in two directions. Finally, the quadratic approximation model is used to constrain the reconstruction objective function and adaptively determine the optimal iteration step size. The compression reconstruction of bearing vibration signals under different health states from multiple experimental platforms has verified the effectiveness of the proposed method.