Non-separable superpositions of polarization and spatial modes in Gaussian beams have shown rich patterns of spatially-variable polarization encoded in the transverse mode of the light, with the potential for many applications. In this work, we investigate encoding similar types of superpositions in Bessel beams. We find that analogously to what is observed in Poincaré-Gaussian beams, Poincaré-Bessel beams can be produced by Bessel-mode superpositions. They show polarization patterns with disclinations in the orientation of the polarization ellipse and mappings of the Poincaré sphere onto the transverse mode. We report on the observation of lemons, stars and monstar disclinations in the multi-ringed profile of Bessel modes. By manipulating the angular spectrum of the component Bessel beams, we are able to impart linear rotation of the patterns along the non-diffracting range due to a linearly increasing propagation phase difference.