A search optimized for new heavy particles decaying to two b-quarks and produced in association with additional b-quarks is reported. The sensitivity is improved by b-tagging at least one lower-pT jet in addition to the two highest-pT jets. The data used in this search correspond to an integrated luminosity of 103 fb-1 collected with a dedicated trijet trigger during the 2017 and 2018 s=13 TeV proton-proton collision runs with the ATLAS detector at the LHC. The search looks for resonant peaks in the b-tagged dijet invariant mass spectrum over a smoothly falling background. The background is estimated with an innovative data-driven method based on orthonormal functions. The observed b-tagged dijet invariant mass spectrum is compatible with the background-only hypothesis. Upper limits at 95% confidence level on a heavy vector-boson production cross section times branching ratio to a pair of b-quarks are derived.