A novel low-complexity wavenumber-domain method is proposed for near-field sensing (NISE). Specifically, the power-concentrated region of the wavenumber-domain channels is related to the target position in a non-linear manner. Based on this observation, a bi-directional convolutional neural network (BiCNN)-based approach is proposed to capture such a relationship, thereby facilitating low-complexity target localization. This method enables direct and gridless target localization using only a limited bandwidth and a single antenna array. Simulation results demonstrate that: 1) during the offline training phase, the proposed BiCNN method can learn to localize the target with fewer trainable parameters compared to the naive neural network architectures; and 2) during the online implementation phase, the BiCNN method can spend 100x less time while maintaining comparable performance to the conventional two-dimensional multiple signal classification (MUSIC) algorithms.