A Bessel beam has the properties of propagation invariance and a self-healing effect, leading to a variety of interesting phenomena and applications. Recently, as a planar diffractive element with miniaturized size, metasurfaces are widely employed to manipulate light in the subwavelength region, including generating a Bessel beam. However, such a metasurface-generated Bessel beam allows output light with no tunable functions. Here, with the interplay of the geometric phase and the dynamic phase, we propose a method to generate and allow conversion from any orthogonal polarizations to independent Bessel beams with a single-layer dielectric metasurface. The simulation results indicate that the arbitrary conversion between different Bessel beams is related to the spin-dependent orbit motion caused by the tight-focusing effect, leading to the singularity of the spot. This physical mechanism is well studied and the theoretical model for revealing the dependence of different incident polarization on the conversion dynamics is presented. Our approach paves a way for efficient generation and multifunctional applications, ranging from high-numerical-aperture devices to compact nanophotonic platforms for spin-dependent structured beams.