Bloch surface waves (BSWs) are electromagnetic surface waves excited in the band gap of a one dimensional dielectric photonic crystal. They are confined at the interface of two media. Due to the use of dielectric material, the losses are very low, which allows the propagation of BSWs over long distances. Another advantage is the possibility of operating within a broad range of wavelengths. In this paper, we study and demonstrate the propagation of light in ultra-thin curved polymer waveguides having different radii fabricated on a BSWs sustaining multilayer. A phase-sensitive multi-parameter near-field optical measurement system (MH-SNOM), which combines heterodyne interferometry and SNOM, is used for the experimental characterization. Propagating properties, bending loss, mode conversion and admixture are investigated. We experimentally show that when light goes through the curved part of the waveguide, energy can be converted into different modes. The superposition and interference of different modes lead to a periodically alternating bright and dark beat phenomenon along the propagation direction. Experimental optical phase and amplitude distributions in the curved waveguide show a very good agreement with simulation results.