We explore the electronic structure and transport properties of a metal on top of a (weakly coupled) two-dimensional topological insulator. Unlike the widely studied junctions between topological nontrivial materials, the systems studied here allow for a unique band structure and transport steering. First, states on the topological insulator layer may coexist with the gapless bulk and, second, the edge states on one edge can be selectively switched off, thereby leading to nearly perfect directional transport of charge and spin even in the zero bias limit. We illustrate these phenomena for Bernal stacked bilayer graphene with Haldane or intrinsic spin-orbit terms and a perpendicular bias voltage. This opens a path for realizing directed transport in materials such as van der Waals heterostructures, monolayer, and ultrathin topological insulators.