  We study the implications of minimal flavor violating low energy
supersymmetry scenarios for the search of new physics in the B and Higgs
sectors at the Tevatron collider and the LHC. We show that the already
stringent Tevatron bound on the decay rate B_s -> mu+ mu- sets strong
constraints on the possibility of generating large corrections to the mass
difference Delta M_s of the B_s eigenstates. We also show that the B_s -> mu+
mu- bound together with the constraint on the branching ratio of the rare decay
b -> s gamma has strong implications for the search of light, non-standard
Higgs bosons at hadron colliders. In doing this, we demonstrate that the former
expressions derived for the analysis of the double penguin contributions in the
Kaon sector need to be corrected by additional terms for a realistic analysis
of these effects. We also study a specific non-minimal flavor violating
scenario, where there are flavor changing gluino-squark-quark interactions,
governed by the CKM matrix elements, and show that the B and Higgs physics
constraints are similar to the ones in the minimal flavor violating case.
Finally we show that, in scenarios like electroweak baryogenesis which have
light stops and charginos, there may be enhanced effects on the B and K mixing
parameters, without any significant effect on the rate of B_s -> mu+ mu-.
