Modeling and rendering dynamic urban driving scenes is crucial for self-driving simulation. Current high-quality methods typically rely on costly manual object tracklet annotations, while self-supervised approaches fail to capture dynamic object motions accurately and decompose scenes properly, resulting in rendering artifacts. We introduce AD-GS, a novel self-supervised framework for high-quality free-viewpoint rendering of driving scenes from a single log. At its core is a novel learnable motion model that integrates locality-aware B-spline curves with global-aware trigonometric functions, enabling flexible yet precise dynamic object modeling. Rather than requiring comprehensive semantic labeling, AD-GS automatically segments scenes into objects and background with the simplified pseudo 2D segmentation, representing objects using dynamic Gaussians and bidirectional temporal visibility masks. Further, our model incorporates visibility reasoning and physically rigid regularization to enhance robustness. Extensive evaluations demonstrate that our annotation-free model significantly outperforms current state-of-the-art annotation-free methods and is competitive with annotation-dependent approaches.