A search for a neutral Higgs boson decaying to a pair of b quarks, and produced in association with at least one additional b quark, is presented. Multijet final states with three jets identified as originating from b quarks, at least one of which may include a non-isolated muon, are studied. The data used in this analysis correspond to an integrated luminosity of 2.7–4.8 fb collected by the CMS experiment in proton–proton collisions at the LHC at a center-of-mass energy of 7 TeV. This search is particularly sensitive to Higgs bosons in scenarios of the Minimal Supersymmetric Model (MSSM) with large values of tanβ. No excess over the predicted background from standard model processes is observed. Stringent upper limits on cross section times branching fraction are derived and interpreted as bounds in the MSSM tanβ and mA parameter-space. Observed 95% confidence level upper limits reach as low as tanβ ≈ 18 for MA ≈ 100 GeV.