Underwater three-dimensional (3D) scanning systems play a crucial role in marine archaeology, offshore engineering, and underwater robotics by capturing detailed representations of areas of interest. However, conventional underwater scanning methods are often time-consuming and inefficient, frequently collecting redundant data points that add little value to the overall representation. This study introduces an artificial intelligence (AI)-driven approach to underwater surface scanning that leverages machine learning techniques such as Bayesian optimisation and Gaussian Process regression to address these inefficiencies. A prototype 3D scanner, controlled by machine learning algorithms, was developed and tested in laboratory conditions that replicated the conditions of offshore deployment. Surfaces with different geometries, including flat, conical, and wavy shapes, were scanned to evaluate the performance of the proposed method against traditional approaches. The new scanning method autonomously selects the most informative measurement locations, reducing the number of scans required while exceeding the accuracy of conventional techniques. The results demonstrate that the proposed approach provides more precise surface representations for most geometries while significantly reducing scanning time. The approach not only reduces computational and storage requirements but also enables efficient data transmission in low-bandwidth scenarios, such as with underwater wireless communication systems. This research highlights the potential of machine learning-enhanced scanning systems to outperform traditional methods, offering a faster, more adaptable, and more accurate solution for underwater visualization in diverse scientific and engineering applications.