  The small mass of the bottom quark, relative to its weak isospin partner, the
top quark, makes the bottom an effective probe of new physics in Higgs and top
sectors. We study the Higgs boson production associated with bottom quarks,
ppbar/pp to phi+b+bbar to 4b, at the Fermilab Tevatron and the CERN LHC. We
find that strong and model-independent constraints on the size of the
phi-b-bbar coupling can be obtained for a wide range of Higgs boson masses.
Their implications for the composite Higgs models with strong dynamics
associated with the third family quarks (such as the top-condensate/topcolor
models with naturally large bottom Yukawa couplings), and for the
supersymmetric models with large tan(beta), are analyzed. We conclude that the
Tevatron and the LHC can put stringent bounds on these models, if the
phi+b+bbar signal is not found.
