Abstract: Shear-wave slowness (DTS) is a key parameter for evaluating rock mechanics and fluid properties, but logging data are often incomplete due to cost or instrument limitations. Conventional machine learning and sequential models struggle with cross-well generalization because of baseline shifts and complex logging environments. This study proposes a locally perceptive bi-directional Mamba network (L-BiMamba) for DTS prediction. The model uses local depthwise separable convolution to capture high-frequency lithological variations, a bi-directional state-space model to encode long-range stratigraphic dependencies, and a bi-directional state-space model to encode long-range stratigraphic dependencies, achieving a deep integration of local micro-mutations and global macro-trends. Experiments on five wells in the Jianyang area, Sichuan Basin, show that L-BiMamba achieved an R² of 0.865, an RMSE of 6.08 μs/ft, and an MAE of 4.24 μs/ft in the blind-well test. Compared with Mamba and BiMamba, L-BiMamba increased R² by 0.048 and 0.017, respectively, and reduced RMSE by 14.1% and 5.7%, respectively. Five-fold blind-well validation further showed that L-BiMamba ranked first in four wells and second in one well, with average R², RMSE, and MAE values of 0.829, 5.58 μs/ft, and 3.94 μs/ft, respectively. These results indicate good cross-well stability within the study area.