  Using a first principles density functional electronic structure method, we
study the energy gaps and magnetism in bilayer graphene nanoribbons as a
function of the ribbon width and the strength of an external electric field
between the layers. We assume AB (Bernal) stacking and consider both armchair
and zigzag edges and two edge alignments distinguished by a 60$^o$ rotation of
one layer with respect to the other. Armchair ribbons exhibit three classes of
bilayer gaps which decrease with increasing ribbon width. An external electric
field between the layers increases the gap in narrow ribbons and decreases the
gap for wide ribbons, a property which can be understood semi-analytically
using a $\pi$-band tight-binding model and perturbation theory. The magnetic
properties of zigzag edge ribbons are different for the two different edge
alignments, and not robust for all exchange-correlation approximations
considered. Bilayer ribbon gaps are sensitive to the presence or absence of
magnetism.
