  Higgs-boson production in association with bottom quarks is an important
discovery channel for supersymmetric Higgs particles at hadron colliders for
large values of tan(beta). We present the complete O(alpha) electroweak and
O(alpha_s) strong corrections to associated bottom-Higgs production through bb
fusion in the MSSM and improve this next-to-leading-order prediction by known
two-loop contributions to the Higgs self-energies, as provided by the program
FeynHiggs. Choosing proper renormalization and input-parameter schemes, the
bulk of the corrections (in particular the leading terms for tan(beta)) can be
absorbed into an improved Born approximation. The remaining non-universal
corrections are typically of the order of a few per cent. Numerical results are
discussed for the benchmark scenarios SPS 1b and SPS 4.
