We present a new simulation for Higgs boson production in association with bottom quarks (bb^-H) at next-to-leading order (NLO) accuracy matched to parton showers in hadronic collisions. Both contributions, the standard one proportional to the bottom-quark Yukawa coupling and the loop-induced one proportional to the top-quark Yukawa coupling from the gluon-fusion process, are taken into account in a scheme with massive bottom quarks. Therefore, we provide the full simulation of the bb^-H final state in the Standard Model, which constitutes also a crucial background to measurements for Higgs-boson pair (HH) production at the Large Hadron Collider when at least one of the Higgs bosons decays to bottom quarks. So far, the modeling of the bb^-H final state induced one of the dominant theoretical uncertainties to HH measurements, as the gluon-fusion component was described only at the leading order (LO) with uncertainties of O(100%). Including NLO corrections in its simulation allows us to reduce the scale dependence to O(50%) so that it becomes subdominant with respect to other systematic uncertainties. As a case study, we provide an in-depth analysis of the bb^-H background to HH measurements with realistic selection cuts in the 2b2γ channel. We also compare our novel simulation with the currently-employed ones, discussing possible issues and shortcomings of a scheme with massless bottom quarks. Finally, we propagate the effect of the new bb^-H simulation to HH searches in the 2b2γ and 2b2τ final states, and we find an improvement of up to 10% (20%) on the current (HL-LHC) limits on σ_SM^HH.