Aiming at the RRT* algorithm in unmanned aerial vehicle (UAV) path planning, there are problems such as poor target bias, slow convergence speed, and tortuous path. This paper introduces an improved Bi-Informed-RRT* algorithm (BPD-APF-Informed-FARRT*), integrating a dual-path balancing operation strategy, a partition-biased sampling strategy, an artificial potential field guidance approach, and a fuzzy adaptive step-size strategy. To begin, the third point between the start and target points is chosen as the middle point, allowing four random trees to be generated at the same time at the start, target, and middle points, hence resolving the delayed convergence issue. Second, the artificial potential field method and the partition-biased sampling strategies are employed in both path generation and optimization phases to guide the placement of new nodes, tackling issues with poor target bias. Then, to address the intricacies of global environments, a fuzzy adaptive step size adjustment strategy is incorporated to boost the exploration efficiency of the growing tree in complex obstacle scenarios. Finally, leveraging the principle of triangular inequality, redundant nodes are removed, and the path is refined using the B-spline curve. Path planning simulation experiments were performed using MATLAB software. The results show that BPD-APF-Informed-FARRT* has more significant advantages in many ways compared with the Bi-RRT*, Informed-RRT*, and Bi-InformedRRT* algorithms. This improved algorithm is a practical and feasible method for solving similar problems.