Seismic anisotropy has widely been used for the characterization of fractures in a reservoir. Recent work has demonstrated the effect of seismic dispersion on producing a frequency-dependent reflection coefficient, which can be important in fracture characterization since large fractures often lead to frequency-dependent anisotropy. In this paper, we examine the impact of anisotropic dispersion on P-wave reflections based on an HTI sand model encased within VTI shale. Although VTI in the overburden does not lead to azimuthal anisotropy, its effect on angle dependence could significantly affect the azimuthal AVO responses at far offsets. We show a modest effect on the amplitude and large effect on the phase, the latter of which could even be mistaken for azimuthal velocity variations. We present a Bayesian inversion based on a forward modelling technique aimed at recovering water saturation, fracture density and fracture length of a HTI sand. Our results show potential of using seismic dispersion in azimuthal AVO analysis to discriminate large-scale fractures from micro-scale cracks.