In models with an enhanced coupling of the Higgs boson to the bottom quark,
the dominant production mechanism in hadronic collisions is often the partonic
sub-process, bg ->bH. We derive the weak corrections to this process and show
that they can be accurately approximated by an "Improved Born Approximation".
At the Tevatron, these corrections are negligible and are dwarfed by PDF and
scale uncertainties for M_H < 200 GeV. At the LHC, the weak corrections are
small for M_H < 500 GeV. For large Higgs boson masses, the corrections become
significant, and are ~18% for M_H ~ 1 TeV at E_CM=10 TeV.