  We analyze the maximum branching ratios for the Flavor Changing Neutral
Current (FCNC) decays of the neutral Higgs bosons of the Minimal Supersymmetric
Standard Model (MSSM) into bottom quarks, h -> b\bar{s} (h=h^0,H^0,A^0). We
consistently correlate these decays with the radiative B-meson decays (b->
s\gamma). A full-fledged combined numerical analysis is performed of these
high-energy and low-energy FCNC decay modes in the MSSM parameter space. Our
calculation shows that the available data on B(b->s \gamma) severely restricts
the allowed values of B(h->b\bar{s}). While the latter could reach a few
percent level in fine-tuned scenarios, the requirement of naturalness reduces
these FCNC rates into the modest range B(h->b\bar{s}) ~ 10^{-4}-10^{-3}. We
find that the bulk of the MSSM contribution to B(h->b\bar{s}) could originate
from the strong supersymmetric sector. The maximum value of the FCNC rates
obtained in this paper disagree significantly with recent (over-)estimates
existing in the literature. Our results are still encouraging because they show
that the FCNC modes h->b\bar{s} can be competitive with other Higgs boson
signatures and could play a helpful complementary role to identify the
supersymmetric Higgs bosons, particularly the lightest CP-even state in the
critical LHC mass region m_{h^0} ~= 90-130 GeV.
