In recent decades, safety has become a priority across numerous engineering domains, prompting the development of strategies and technologies to address safety, risk, and reliability challenges. Among these, Machine Learning (ML) and Deep Learning (DL) have emerged as powerful tools, offering diverse algorithms adaptable to a wide range of applications. However, the resulting body of literature is vast and fragmented, with most existing reviews and bibliometric studies focusing on specific areas rather than providing a comprehensive overview. This study addresses that gap by conducting a Systematic Bibliometric Analysis (SBA) to deliver a holistic understanding of ML and DL applications in safety-related research. The analysis explores core research areas, application domains, key contributors, influential studies, and temporal trends. The results highlight several prominent application fields, including rotating equipment, structural health monitoring, battery systems, aero engines, and turbines. Over the past four years, DL techniques have shown significant growth in adoption, complemented by emerging approaches such as deep reinforcement learning. These advancements reflect the increasing integration of AI-driven methods into safety engineering, enhancing predictive capabilities and decision-making processes. In addition to mapping the research landscape, this paper proposes a practical workflow for conducting SBAs, designed to be replicable and adaptable for various disciplines. By providing structured guidelines, the workflow supports systematic literature exploration, helping researchers identify knowledge gaps, emerging trends, and collaboration opportunities. The findings underscore the evolving role of ML and DL in safety science, offering insights for both academic researchers and industry practitioners. Beyond safety-focused applications, the proposed SBA framework holds potential benefits for other domains where systematic knowledge mapping is essential.