  Bilayer graphene with an interlayer potential difference has an energy gap
and, when the potential difference varies spatially, topologically protected
one-dimensional states localized along the difference's zero-lines. When
disorder is absent, electronic travel directions along zero-line trajectories
are fixed by valley Hall properties. Using the Landauer-B\"uttiker formula and
the non-equilibrium Green's function technique we demonstrate numerically that
collisions between electrons traveling in opposite directions, due to either
disorder or changes in path direction, are strongly suppressed. We find that
extremely long mean free paths of the order of hundreds of microns can be
expected in relatively clean samples. This finding suggests the possibility of
designing low power nanoscale electronic devices in which transport paths are
controlled by gates which alter the inter-layer potential landscape.
