Proximity orbital and spin-orbit effects of bilayer graphene on monolayer WSe2 are investigated from first principles. We find that the built-in electric field induces an orbital band gap of about 10 meV in bilayer graphene. Remarkably, the proximity spin-orbit splitting for holes is 2 orders of magnitude—the spin-orbit splitting of the valence band at K is about 2 meV—more than for electrons. Effectively, holes experience spin valley locking due to the strong proximity of the lower graphene layer to WSe2. However, applying an external transverse electric field of some 1  V/nm, countering the built-in field of the heterostructure, completely reverses this effect and allows, instead of holes, electrons to be spin valley locked with 2 meV spin-orbit splitting. Such a behavior constitutes a highly efficient field-effect spin-orbit valve, making bilayer graphene on WSe2 a potential platform for a field-effect spin transistor.