  We show that a simple and accurate approach to the computation of hadron
collider processes involving initial-state $b$ quarks can be obtained by
introducing an independently parametrized b PDF. We use the so-called FONLL
method for the matching of a scheme in which the b quark is treated as a
massless parton to that in which it is treated as a massive state, and extend
it to the case in which the b quark PDF is not necessarily determined by
perturbative matching conditions. This generalizes to hadronic collisions
analogous results previously obtained for deep-inelastic scattering. The
results corresponds to a `massive b' scheme, in which b mass effects are
retained, yet the b quark is endowed with a PDF. We specifically study Higgs
production in bottom fusion, and show that our approach overcomes difficulties
related to the fact that in a standard massive four-flavor scheme b-quark
induced processes only start at high perturbative orders.
