The Job Shop Scheduling Problem (JSSP) is a complex combinatorial optimization problem. There has been growing interest in using online Reinforcement Learning (RL) for JSSP. While online RL can quickly find acceptable solutions, especially for larger problems, it produces lower-quality results than traditional methods like Constraint Programming (CP). A significant downside of online RL is that it cannot learn from existing data, such as solutions generated from CP, requiring them to train from scratch, leading to sample inefficiency and making them unable to learn from more optimal examples. We introduce Offline Reinforcement Learning for Learning to Dispatch (Offline-LD), a novel approach for JSSP that addresses these limitations. Offline-LD adapts two CQL-based Q-learning methods (mQRDQN and discrete mSAC) for maskable action spaces, introduces a new entropy bonus modification for discrete SAC, and exploits reward normalization through preprocessing. Our experiments show that Offline-LD outperforms online RL on both generated and benchmark instances. By introducing noise into the dataset, we achieve similar or better results than those obtained from the expert dataset, indicating that a more diverse training set is preferable because it contains counterfactual information.