This paper describes a study of techniques for identifying Higgs bosons at high transverse momenta decaying into bottom-quark pairs, $H\to bb¯$, for proton-proton collision data collected by the ATLAS detector at the Large Hadron Collider at a centre-of-mass energy $s=13$ TeV. These decays are reconstructed from calorimeter jets found with the anti-$kt$ $R=1.0$ jet algorithm. To tag Higgs bosons, a combination of requirements is used: $b$-tagging of $R=0.2$ track-jets matched to the large-$R$ calorimeter jet, and requirements on the jet mass and other jet substructure variables. The Higgs boson tagging efficiency and corresponding multijet and hadronic top-quark background rejections are evaluated using Monte Carlo simulation. Several benchmark tagging selections are defined for different signal efficiency targets. The modelling of the relevant input distributions used to tag Higgs bosons is studied in 36 fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ of data collected in 2015 and 2016 using $g\to bb¯$ and $Z(\to bb¯)\gamma$ event selections in data. Both processes are found to be well modelled within the statistical and systematic uncertainties.