Recognizing the potential transformative impact on transportation systems, safety perceptions of Shared Automated Vehicles (SAVs) have gained significant attention from researchers in recent years. Yet, the critical factors influencing perception changes and the willingness to re-ride (WTR) have not been extensively studied despite their relevance to SAV operations. This study applied Bayesian Networks (BNs) and Text Network (TN) methodologies to analyze survey data from a shared automated passenger shuttle (SAPS) pilot program conducted between March and April 2023, at Fred G. Bond Metro Park in Cary, North Carolina. Participants in the survey provided feedback on their safety perceptions of the SAPS before and after riding, as well as their willingness to ride again. Key findings reveal that shuttle operations, especially timely arrival and drop-off, significantly affect both perceptional change and WTR. Furthermore, users who accessed the shuttle by walking, biking, or public transportation were more likely to positively change their perception and express a willingness to ride the shuttle again. Also, individuals with initial perceptions of the SAPS as very unsafe or unsafe showed a higher likelihood of perception change. Conversely, older respondents were less likely to experience safety perception changes and WTR. Text network analysis further illuminated that the primary motivations for WTR were the enjoyable experience and convenience offered by the shuttle. The study contributes to the growing body of literature on SAVs by providing practical implications for the future development and testing of SAPSs. These insights are invaluable for policymakers and planners in optimizing SAPS operations, providing a deeper understanding of user experiences and expectations.