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, (Formula presented) at the Fermilab Tevatron and the CERN LHC. We find that strong and model-independent constraints on the size of the (Formula presented) 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-quark condensate or top-color models with naturally large bottom Yukawa couplings), and for the supersymmetric models with large (Formula presented) are analyzed. We conclude that the Tevatron and the LHC can put stringent bounds on these models, if the (Formula presented) signal is not found.