  We compute the branching fractions of B_{s,d} -> l+ l- in the type-II
two-Higgs-doublet model with large tan(beta). We find that the parameters of
the neutral Higgs sector of the two-Higgs-doublet model cancel in the result,
so that the branching fractions depend only on the charged Higgs mass and
tan(beta). For large values of tan(beta) and a charged Higgs mass above the
bound from b -> s gamma, we find that the branching fractions can be enhanced
by up to an order of magnitude or suppressed by up to a factor of two compared
to the Standard Model result. We point out that previous calculations in the
literature are gauge-dependent due to the omission of an important diagram,
which gives the dominant contribution in the 't Hooft-Feynman gauge. We have
analyzed in detail the region of the (M_{H^+}, tan(beta)) plane to be probed by
searches for B_s -> mu+ mu- in Run II of the Tevatron. Since the branching
fraction increases like tan^4(beta), this decay mode is complementary to b -> s
gamma and efficiently probes the large tan(beta) region. For tan(beta)=60, an
integrated luminosity of 20 fb^{-1} in an extended Run II will probe charged
Higgs masses up to 260 GeV, if the background to B_s -> mu+ mu- is small. For
the same value of tan(beta), the LHC may be able to explore charged Higgs
masses up to 1 TeV using this decay.
