  Using the B\"{u}ttiker-Landauer formulation of transport theory in the linear
response regime, the valley currents and non-local resistances of bilayer
graphene nanostructures with broken inversion symmetry are calculated. It is
shown that broken inversion symmetry in bilayer graphene nanostructures leads
to striking enhancement of the non-local 4-terminal resistance and to valley
currents several times stronger than the conventional electric current when the
Fermi energy is in the spectral gap close to the energy of Dirac point. The
scaling relation between local and non-local resistances is investigated as the
gate voltage varies at zero Fermi energy and a power-law is found to be
satisfied. The valley velocity field and valley accumulation in four-terminal
bilayer graphene nanostructures are evaluated in the presence of inversion
symmetry breaking. The valley velocity and non-local resistance are found to
scale differently with the applied gate voltage. The unit cell-averaged valley
accumulation is found to exhibit a dipolar spatial distribution consistent with
the accumulation arising from the valley currents. We define and calculate a
{\em valley capacitance} that characterizes the valley accumulation response to
voltages applied to the nanostructure's contacts.
