Robotic systems are transforming image-guided interventions by enhancing accuracy and minimizing radiation exposure. A significant challenge in robotic assistance lies in surgical path planning, which often relies on the registration of intraoperative 2D images with preoperative 3D CT scans. This requirement can be burdensome and costly, particularly in procedures like vertebroplasty, where preoperative CT scans are not routinely performed. To address this issue, we introduce a differentiable rendering-based framework for 3D transpedicular path planning utilizing bi-planar 2D X-rays. Our method integrates differentiable rendering with a vertebral atlas generated through a Statistical Shape Model (SSM) and employs a learned similarity loss to refine the SSM shape and pose dynamically, independent of fixed imaging geometries. We evaluated our framework in two stages: first, through vertebral reconstruction from orthogonal X-rays for benchmarking, and second, via clinician-in-the-loop path planning using arbitrary-view X-rays. Our results indicate that our method outperformed a normalized cross-correlation baseline in reconstruction metrics (DICE: 0.75 vs. 0.65) and achieved comparable performance to the state-of-the-art model ReVerteR (DICE: 0.77), while maintaining generalization to arbitrary views. Success rates for bipedicular planning reached 82% with synthetic data and 75% with cadaver data, exceeding the 66% and 31% rates of a 2D-to-3D baseline, respectively. In conclusion, our framework facilitates versatile, CT-free 3D path planning for robot-assisted vertebroplasty, effectively accommodating real-world imaging diversity without the need for preoperative CT scans.