The collinear acousto-optical transformation of Bessel light beams in biaxial gyrotropic crystals into two annular, internal conical refraction beams with orthogonal elliptical polarization is studied. It is found that the diffraction efficiency is maximal (~50–60%) for low ultrasound intensities and varies slightly with further increases in acoustic power. At high ultrasound intensities, the intensities of the transmitted and diffracted annular beams differ insignificantly. The possible use of this acousto-optical interaction for creating collinear tuneable narrow-band acousto-optical filters at low ultrasonic frequencies is demonstrated.