We investigate the shift-current response of inversion-broken AB-stacked bilayer graphene under in-plane and perpendicular magnetic fields, from the perturbative regime to strong orbital quantization, in both two-dimensional bulk systems and finite nanoribbons. An in-plane field enters through opposite momentum shifts in the two layers and leaves the bulk band dispersion essentially unchanged, producing only a modest, frequency-dependent redistribution of the shift-current spectrum. A weak perpendicular field is treated using a gauge-covariant Peierls expansion. The resulting band corrections are concentrated near Berry-curvature hot spots, although the dominant shift-current transitions occur elsewhere, and the valley-summed response is even in the field with a leading quadratic correction. At strong perpendicular field, a rational-flux magnetic supercell reveals nearly flat Landau-level-like bulk bands and a greatly enhanced density of states, yet the bulk shift current is almost completely quenched because the relevant optical matrix elements and shift-vector contributions are suppressed or cancel. Finite ribbons retain optically active boundary channels: in zigzag ribbons, magnetic reconstruction turns edge-derived states from dark states into bright photovoltaic channels, with the associated peak scaling inversely with ribbon width. These results show that magnetic control of the nonlinear photovoltaic response is governed by wave-function reconstruction and quantum-geometric matrix elements rather than by the density of states alone.