We show that gated bilayer graphene zigzag ribbons possess a fast and a slow edge, characterized by edge-state velocities that differ due to non-negligible next-nearest-neighbor hopping elements. By applying bosonization and renormalization group methods, we find that the slow edge can acquire a sizable interaction-induced gap, which is tunable via an external gate voltage Vg. In contrast to the gate-induced gap in the bulk, the interaction-induced gap depends nonmonotonously on the on-site potential V.