A search is described for the production of a pair of bottom-type vector-like quarks (VLQs), each decaying into a \PQb quark and either a Higgs or a \PZ boson. The analysis is based on data from proton-proton collisions at a 13\TeV center-of-mass energy recorded by the CMS experiment, corresponding to a total integrated luminosity of 137\fbinv. Since the predominant decay modes of the Higgs and \PZ bosons are to a pair of quarks, the analysis focuses on final states consisting of jets resulting from the six quarks produced in the events. Because the two jets produced in the decay of a highly boosted Higgs or \PZ boson might merge to form a single jet, three independent analyses are performed, categorized by the number of observed jets. No signal in excess of the expected background is observed, allowing lower limits to be set on the VLQ mass. The limits at 95\% confidence level are 1573\GeV in the case where the VLQ decays exclusively to a b quark and a Higgs boson, 1394\GeV for when it decays exclusively to a b quark and a \PZ boson, and 1449\GeV for when it decays equally in these two modes.