For a partially coherent Bessel-Gaussian (PCBG) vortex beam, information regarding the topological charge (TC) is hidden in the phase of the cross-spectral density (CSD) function. We theoretically and experimentally confirmed that during free-space propagation, the number of coherence singularities is equal to the magnitude of the TC. In contrast to the Laguerre-Gaussian vortex beam, this quantitative relationship only holds for the case with an off-axis reference point for the PCBG vortex beam. The phase winding direction is determined by the sign of the TC. We developed a scheme for CSD phase measurement of PCBG vortex beams and verified the aforementioned quantitative relationship at different propagation distances and coherence widths. The findings of this study may be useful for optical communications.