Many patients face difficulties when accessing medical facilities, particularly in rural areas. To alleviate these concerns, medical centers may offer transportation to eligible patients. However, the operation of such services is typically not tightly coordinated with the scheduling of medical appointments. Motivated by our collaborations with the U.S. Veterans Health Administration, we propose an integrated approach that simultaneously considers patient routing and operating room scheduling decisions. We model this problem as a mixed-integer program. Unfortunately, realistically sized instances of this problem are intractable, so we focus on a special case of the problem that captures the needs of low-volume (e.g., rural) hospitals. We establish structural properties that are exploited to develop a branch-and-price algorithm, which greatly outperforms a commercial solver on the original formulation. We discuss several algorithmic strategies to improve the overall solution efficiency. We evaluate the performance of the proposed approach through an extensive computational study calibrated with clinical data. Our results demonstrate that there exist opportunities for healthcare providers to significantly improve the quality of their services by integrating scheduling and routing decisions.