In ocean monitoring, the identification and tracking of ship wakes are crucial. Ship wakes are difficult to physically characterize because they are complicated multiphase combinations. It is possible to efficiently analyze the scattering features of ship-induced bubble wakes by utilizing the excellent penetrating capabilities of blue-green lasers in seawater. Bessel-Gaussian (BG) beam propagation properties are determined in this work by using the rigorous angular spectrum diffraction theory. An analytical equation for the beam shape coefficient of BG beams is derived by combining the integral local approximation approach with the generalized Lorenz-Mie theory (GLMT). Therefore, differences in the scattering properties of BG beams passing through ship bubble waves are therefore investigated systematically. The results demonstrate that the scattering efficiency factor for a single spherical bubble particle shows clear resonance peaks as the size parameter grows, and the peak values decrease significantly when the beam topological charge increases. Meanwhile, as the beam topological charge, beam waist radius, and cone angle increase, the differential scattering cross section decreases. Similar effects of the differential scattering cross section on the beam topological charge, beam waist radius, and cone angle are also seen for the collective bubble wake. This work provides theoretical support for relevant applications in ocean target identification and monitoring, as well as a theoretical foundation for studying the scattering characteristics of ship-induced bubble wakes.