Fine-grained modeling of driving styles is critical for decision making in autonomous driving. However, existing methods are constrained by the high cost of manual labeling and a lack of interpretability. This study proposes an unsupervised disentanglement framework based on a variational autoencoder (VAE), which, for the first time, enables the automatic extraction of interpretable driving style representations from car-following trajectories. The key innovations of this work are threefold: (1) a dual-decoder VAE architecture is designed, leveraging driver identity as a proxy label to guide the learning of the latent space; (2) self-dynamics and interaction dynamics features are decoupled, with an attention mechanism employed to quantify the influence of the lead vehicle; (3) a bidirectional interpretability verification framework is established between latent variables and trajectory behaviors. Evaluated on a car-following dataset comprising 25 drivers, the model achieves a Driver Identification accuracy of 98.88%. Mutual information analysis reveals the physical semantics encoded in major latent dimensions. For instance, latent dimension z₂₂ is strongly correlated with the minimum following distance and car-following efficiency. One-dimensional latent traversal further confirms that individual dimensions modulate specific behavioral traits: increasing z₂₂ improves safety margins by 18% but reduces efficiency by 23%, demonstrating that it encodes a trade-off between safety and efficiency. This work provides a controllable representation framework for driving style transfer in autonomous systems and offers a more granular approach for analyzing driver behavior in car-following scenarios, with potential for extension to broader driving contexts.