  Higgs singlet superfields, usually present in extensions of the Minimal
Supersymmetric Standard Model (MSSM) which address the $\mu$-problem, such as
the Next-to-Minimal Supersymmetric Standard Model (NMSSM) and the Minimal
Nonminimal Supersymmetric Standard Model (mnSSM), can have significant
contributions to $B$-meson flavour-changing neutral current observables for
large values of $\tan\beta \gsim 50$. Illustrative results are presented
including effects on the $B_s$ and on the rare decay $B_s\to\mu^+\mu^-$. In
particular, we find that in the NMSSM, the branching ratio for
$B_s\to\mu^+\mu^-$ can be enhanced or even suppressed with respect to the
Standard Model prediction by more than one order of magnitude.
