Abstract: Offshore wind power has been the fastest-growing form of renewable energy for the last few years, owing to its effectiveness in achieving carbon neutrality through a reasonable and efficient utilization of wind power resources. With offshore wind farms gradually developing into the deep and far sea, greater attention is paid to the bearing characteristics of foundations for offshore wind turbines. Therefore, it becomes significantly important to explore new foundations, effectively promoting the development of offshore wind power. Numerous researchers have substantially investigated novel foundations for offshore wind turbines to help with offshore wind farm construction. Compared to other foundations, the pile–bucket composite foundation has obvious advantages in terms of bearing performance. In this paper, a series of numerical calculation models for pile–bucket composite foundations in heterogeneous saturated clay are established using the finite element software ABAQUS. Additionally, the undrained shear strength changes with depth are examined via field variables to explain soil heterogeneity in the finite element model. Next, the displacement control method is adopted to apply the vertical loading V, horizontal loading H, and bending moment M at the top of the foundation. Simultaneously, the ultimate bearing capacity of the foundations is obtained by the double tangent method, and the bearing capacity factors of each load direction are obtained by normalizing the ultimate bearing capacity in different calculations. To obtain the preliminary design method for the size of pile–bucket composite foundation, the priority of influencing factors is studied through the orthogonal test. The results show that the saturated clay coefficient K has a nominal effect on the vertical bearing capacity coefficient N_cV. When K is different, N_cV remains almost unchanged for a certain foundation. Concerning the impact of bucket shapes on the bearing capacity coefficient in three directions, great interaction is observed between the diameter D and the buried depth L of the bucket structure. The diameter of the bucket has the greatest influence on the bearing characteristics of the pile–bucket composite foundations, wherein increasing the former can significantly improve the latter. The research results provide a reference for the design of the pile–bucket composite foundation of an offshore wind turbine.