  We explore the sensitivity of flavour changing b -> s transitions to a
(sub-)GeV hidden sector with generic couplings to the Standard Model through
the Higgs, vector and axion portals. The underlying two-body decays of B
mesons, B -> X_s S and B0 -> SS, where S denotes a generic new GeV-scale
particle, may significantly enhance the yield of monochromatic lepton pairs in
the final state via prompt decays of S to a dilepton pair. Existing
measurements of the charged lepton spectrum in neutral-current semileptonic B
decays provide bounds on the parameters of the light sector that are
significantly more stringent than the requirements of naturalness. New search
modes, such as B -> X_s + n(l+l-) and B0 -> n(l+l-) with n > 1 can provide
additional sensitivity to scenarios in which both the Higgs and vector portals
are active, and are accessible to (super-)B factories and hadron colliders.
