We investigate the prospects for the discovery at the CERN Large Hadron Collider or at the Fermilab Tevatron of neutral Higgs bosons through the channel where the Higgs are produced together with a single bottom quark and the Higgs decays into a pair of tau leptons, $bg to bphi^0 to btau^+tau^-, phi^0 = h^0, H^0, A^0$. We work within the framework of the minimal supersymmetric model. The dominant physics background from the production of $btau^+tau^-$, $jtau^+tau^-$ ($j = g, u, d, s, c$), $bbar{b}W^+W^-$, $W+2j$ and $Wbj$ is calculated with realistic acceptance cuts and efficiencies. Promising results are found for the CP-odd pseudoscalar ($A^0$) and the heavier CP-even scalar ($H^0$) Higgs bosons with masses up to one TeV.