In this work, we address the task of point cloud denoising using a novel framework adapting Diffusion Schrödinger bridges to unstructured data like point sets. Unlike previous works that predict point-wise displacements from point features or learned noise distributions, our method learns an optimal transport plan between paired point clouds. In experiments on object datasets such as the PU-Net dataset and real-world datasets like ScanNet++ and ARKitScenes, P2P-Bridge improves by a notable margin over existing methods. Although our method demonstrates promising results utilizing solely point coordinates, we demonstrate that incorporating additional features like RGB information and point-wise DINOV2 features further improves the results. Code will be made public upon acceptance.