A search for neutral Higgs bosons decaying into a (b\overline{b}) quark pair and produced in association with at least one additional b quark is presented. This signature is sensitive to the Higgs sector of the minimal supersymmetric standard model (MSSM) with large values of the parameter tan β. The analysis is based on data from proton-proton collisions at a center-of-mass energy of 8 TeV collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 19.7 fb⁻¹. The results are combined with a previous analysis based on 7 TeV data. No signal is observed. Stringent upper limits on the cross section times branching fraction are derived for Higgs bosons with masses up to 900 GeV, and the results are interpreted within different MSSM benchmark scenarios, (m_h^{max}), (m_h^{mod+}), (m_h^{mod−}), light-stau and light-stop. Observed 95% confidence level upper limits on tan β, ranging from 14 to 50, are obtained in the (m_h^{mod+}) benchmark scenario.