A search for pair production of bottom squarks in events with hadronically decaying t-leptons, b-tagged jets, and large missing transverse momentum is presented. The analyzed dataset is based on proton-proton collisions at root s = 13 TeV delivered by the Large Hadron Collider and recorded by the ATLAS detector from 2015 to 2018, and corresponds to an integrated luminosity of 139 fb(-1). The observed data are compatible with the expected Standard Model background. Results are interpreted in a simplified model where each bottom squark is assumed to decay into the second-lightest neutralino (chi) over tilde (0)(2) and a bottom quark, with (chi) over tilde (0)(2) decaying into a Higgs boson and the lightest neutralino (chi) over tilde1(0). The search focuses on final states where at least one Higgs boson decays into a pair of hadronically decaying t-leptons. This allows the acceptance and thus the sensitivity to be significantly improved relative to the previous results at low masses of the (chi) over tilde (0)(2), where bottom-squark masses up to 850 GeV are excluded at the 95% confidence level, assuming a mass difference of 130 GeV between (chi) over tilde (0)(2) and (chi) over tilde (0)(1). Model-independent upper limits are also set on the cross section of processes beyond the Standard Model.