In this paper, we introduce movable antenna (MA) technology into orthogonal time frequency space (OTFS) systems to enable wavelength-level antenna position optimization under imperfect channel state information (CSI), thereby mitigating deep fading. To accurately acquire CSI, we develop a sparse Bayesian learning method with variational inference (SBLVI) method. Based on estimated CSI, we formulate an MA position optimization problem with the objective of maximizing channel gain. Due to the highly non-convex character of the problem, we further develop a deep reinforcement learning (DRL) strategy to intelligently optimize MA positions. Simulation results show that the proposed SBLVI method significantly improves channel estimation accuracy over benchmark methods, and MA position optimization based on estimated CSI achieves substantially higher channel gains than the fixed-position antenna (FPA), demonstrating the effectiveness of the proposed MA-assisted OTFS system.