  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-$p_{\rm{T}}$ jet in addition to
the two highest-$p_{\rm{T}}$ jets. The data used in this search correspond to
an integrated luminosity of 103 $\text{fb}^{-1}$ collected with a dedicated
trijet trigger during the 2017 and 2018 $\sqrt{s} = 13$ 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.
