Time series classification an important and challenging real-world problem and has been extensively studied by deep learning methods. However, the non-stationary property of time series data hinders further improvement. Thus domain generalization technique has been introduced due to such property, and existed methods adopted domain generalization have overlooked the potential mutual dependency between domain-invariant and domain-specific representations. In response, we present bidirectional dependency representation disentanglement for generalization (BiRep), a novel approach to time series classification that leverages the power of transfer learning through domain generalization to enhance model generalizability by disentangling domain-specific and domain-invariant representations using a single GPT-2 backbone with prompt tuning, thus improving classification accuracy. Extensive experiments on various gesture recognition and human activity datasets demonstrate the superior performance of BiRep compared to other related methods, highlighting its robustness and effectiveness in handling diverse and unseen data distributions.