A search for dark matter (DM) particles produced in association with bottom quarks is presented. The analysis uses proton-proton collision data at a center-of-mass energy of $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The search is performed in the final state with large missing transverse momentum and a pair of jets originating from bottom quarks. No significant excess of data is observed with respect to the standard model expectation. Results are interpreted in the context of a type-II two-Higgs-doublet model with an additional light pseudoscalar (2HDM+a). An upper limit is set on the mass of the lighter pseudoscalar, excluding masses up to 260 GeV at 95% confidence level. This is the first search at the LHC to probe DM produced in association with two nonresonant bottom quarks in the 2HDM+a model. Sensitivity to the parameter space with the ratio of the vacuum expectation values of the two Higgs doublets, $\tan\beta$, greater than 15 is achieved, capitalizing on the enhancement of couplings between pseudoscalars and bottom quarks with high $\tan\beta$.