  We show that the spectrum of subbands in an electrostatically defined quantum
wire in gapped bilayer graphene directly manifests the minivalley structure and
reflects Berry curvature via the associated magnetic moment of the states in
the low-energy bands of this two-dimensional material. We demonstrate how these
appear in degeneracies of the low-energy minibands and their valley splitting,
which develops linearly in a weak magnetic field. Consequently,
magneto-conductance of a ballistic point contact connecting two non-gapped
areas of a bilayer through a gapped (top and bottom gated) barrier would
reflect such degeneracies by the heights of the first few conductance steps
developing upon the increase of the doping of the BLG conduction channel:
$8e^2/h$ steps in a wide channel in BLG with a large gap, $4e^2/h$ steps in
narrow channels, all splitting into a staircase of $2e^2/h$ steps upon lifting
valley degeneracy by a magnetic field.
