Mature faults with large cumulative slip often separate rocks with dissimilar elastic properties and show asymmetric damage distribution. Elastic contrast across such bimaterial faults can significantly modify various aspects of earthquake rupture dynamics, including normal stress variations, rupture propagation direction, distribution of ground motions, and evolution of off-fault damage. Thus, analyzing elastic contrasts of bimaterial faults is important for understanding earthquake physics and related hazard potential. The effect of elastic contrast between isotropic materials on rupture dynamics is relatively well studied. However, most fault rocks are elastically anisotropic, and little is known about how the anisotropy affects rupture dynamics. We examine microstructures of the Sandhill Corner shear zone, which separates quartzofeldspathic rock and micaceous schist with wider and narrower damage zones, respectively. This shear zone is part of the Norumbega fault system, a Paleozoic, large-displacement, seismogenic, strike-slip fault system exhumed from mid-crustal depths. We calculate elastic properties and seismic wave speeds of elastically anisotropic rocks from each unit having different proportions of mica grains aligned sub-parallel to the fault. Our findings show that the horizontally polarized shear wave propagating parallel to the bimaterial fault (with fault-normal particle motion) is the slowest owing to the fault-normal compliance and therefore may be important in determining the elastic contrast that affects rupture dynamics in anisotropic media. Following results from subshear rupture propagation models in isotropic media, our results are consistent with ruptures preferentially propagated in the slip direction of the schist, which has the slower horizontal shear wave and larger fault-normal compliance.