The unusual electronic properties of edges in graphene-based systems originate from the pseudospinorial character of their electronic wavefunctions associated with their non-trivial topological structure. This is manifested by the appearance of pronounced zero-energy electronic states localized at the material zigzag edges that are expected to have a significant contribution to the interlayer transport in such systems. In this work, we utilize a unique experimental setup and electronic transport calculations to quantitatively distinguish between edge and bulk transport, showing that their relative contribution strongly depends on the angular stacking configuration and interlayer potential. Furthermore, we find that, despite of the strong localization of edge state around the circumference of the contact, edge transport in incommensurate interfaces can dominate up to contact diameters of the order of 2 μm, even in the presence of edge disorder. The intricate interplay between edge and bulk transport contributions revealed in the present study may have profound consequences on practical applications of nanoscale twisted graphene-based electronics.