Extremely large antenna arrays and high-frequency operation are two key technologies that advance performance metrics such as higher data rates, lower latency, and wider coverage in sixth-generation communications. However, the adoption of these technologies fundamentally changes the characteristics of wavefronts, forcing communication systems to operate in the near-field region. The transition from planar far-field communications to spherical near-field propagation necessitates novel channel estimation algorithms to fully exploit the unique features of spherical wavefronts for advanced transceiver design. To this end, we propose a novel semi-gridless channel estimation approach based on a variational Bayesian (VB) inference framework. Specifically, we reformulate the near-field channel model for both uniform linear arrays and uniform planar arrays into separate direction-of-arrival (DoAs) and distance components. Building on these new representations, we employ a gridless approach for DoAs estimation using a von Mises distribution, and a coarse-to-fine grid search for distance estimation. We then develop a semi-gridless variational Bayesian (SG-VB) algorithm with efficient update rules that enables accurate channel reconstruction. Simulation results validate the effectiveness of the proposed SG-VB algorithm, demonstrating enhanced near-field channel reconstruction accuracy and superior estimation performance for both DoAs and distance components embedded in near-field channels.