In base-station-based underwater wireless acoustic networks (B-UWANs), effective handover mechanisms are necessary to ensure seamless data services for mobile nodes such as autonomous underwater vehicles (AUVs). Unlike terrestrial base stations (BSs), moored buoy BSs in B-UWANs experience motion responses due to wave loads under environmental conditions, posing unique challenges to the handover process. This study examines how BS motion affects handover decision errors, which arise when AUVs incorrectly initiate handovers to unintended BSs due to BS motion. By utilizing the AUV–BS distance as a handover triggering parameter, our analysis reveals a significant increase in decision errors within the overlapping regions when both the current and target BSs are in motion, especially when moving in the same direction. In addition, these errors intensify with the magnitude of BS motion and are exacerbated by smaller BS network radii. Based on these simulation results, we present an analytical framework that not only measures the influence of BS motion on the AUV–BS distance but also provides strategic insights for refining underwater handover protocols, thereby enhancing operational reliability and service continuity in B-UWANs.