<p>Fuzzy graph theory has recently received a lot of interest due to its wide range of applications, and researchers are working hard to build specific topological indices for them. The Sombor index is a significant instance of such an index, particularly for the discipline of chemistry. In a bipolar fuzzy network, nodes and edges have opposing viewpoints, allowing for the quantification of uncertainty from positive as well as negative perspectives for each node and edge. This study introduces the Sombor index for bipolar fuzzy graphs (BFGs). It covers its bounded nature, upper and lower limits, and the impact of removing vertices or edges, providing valuable insights into graph dynamics and structural alterations. This article investigates the Sombor index for BFGs and their subgraphs, highlighting their key properties. It explores isomorphic characteristics and analyzes the upper and lower bounds of the Sombor index within the framework of BFGs. Additionally, the study presents the Sombor index for directed BFGs and derives formulas for calculating the Sombor index for different classes of regular BFGs and bipolar fuzzy cycles. Furthermore, it establishes the relationship between the Sombor index of BFGs and various indices associated with BFGs. Finally, a fundamental understanding of bipolar fuzzy graphs facilitates the application of the Sombor index in mutual fund investment decision-making using Multi-Attribute Decision-Making (MADM) techniques, along with its comparison to AHP and TOPSIS methods, and enables a comprehensive analysis of the top six countries affected by human trafficking.</p>