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Composite bucket foundation (CBF) is an environmentally friendly form of offshore wind power foundation. By virtue of the air-floating subdivision structure in the bucket, the foundation has a self-floating characteristic and can allow for long-distance air-floating towing and transport. In this study, first, a numerical analysis was performed on the towing motion characteristics of CBF, and the formula for foundation stability was deduced; then, we probed into the variation rules of the natural period of the foundation with draft and analyzed the response amplitude operator (RAO) responses, added mass coefficients, radiation damping coefficients, and exciting forces (moments) of the composite bucket foundation under different drafts and different wave directions. Finally, we clarified the basic hydrodynamic characteristics of the composite bucket foundation in the frequency domain and adopted multiple random wave models to investigate the effects of different wave heights, periods, and spectral peak factors on the towing motion characteristics of composite bucket foundation.