A search is presented for single production of a vector-like B quark decaying into a Standard Model b-quark and a Standard Model Higgs boson, which decays into a b-b pair. The search is carried out in 139 fb-1 of SQUARE ROOT s = 13TeV proton-proton collision data collected by the ATLAS detector at the LHC between 2015 and 2018. No significant deviation from the Standard Model background prediction is observed, and mass-dependent exclusion limits at the 95% confidence level are set on the resonance production cross-section in several theoretical scenarios determined by the couplings cW, cZ and cH between the
B quark and the Standard Model W, Z and Higgs bosons, respectively. For a vector-like
B occurring as an isospin singlet, the search excludes values of cW greater than 0.45 for a
B resonance mass (mB) between 1.0 and 1.2TeV. For 1.2TeV < mB < 2.0TeV, cW values larger than 0.50-0.65 are excluded. If the B occurs as part of a (B, Y ) doublet, the smallest excluded cZ coupling values range between 0.3 and 0.5 across the investigated resonance mass range 1.0TeV < mB < 2.0TeV.