In isotropic bistable media a vortex pair typically evolves into rotating spiral waves. In an anisotropic system instead of spiral waves the vortices can form wave fragments that propagate with a constant speed in a given direction determined by the system's anisotropy. The fragments may propagate invariably, shrink, or expand. We develop a kinematic approach for the study of vortex-pair dynamics in anisotropic bistable media and use it to capture the wave fragment dynamics.