This paper discusses features of the acousto-optic interaction of Bessel light beams and acoustic beams in transversely isotropic crystals. The main characteristics of this type of diffraction are considered, including an analysis of possible vector diagrams of the acousto-optic process, the choice of the interaction geometry in actual crystals, and the role of longitudinal and transverse matching, as well as the derivation and solution of shortened equations. It is shown that high diffraction efficiency is maintained when there is a transition from plane waves to Bessel acoustic beams, and the possibility also appears of dynamically reconstructing the cone angle of a diffracted Bessel light beam. Moreover, in the process of this diffraction, there is a transformation of the order of the Bessel functions and accordingly of the order of the screw dislocation of the phase front of the light field within wide limits.