A search for the exotic decay of the Higgs boson (H) into a b (b) over bar resonance plus missing transverse momentum is described. The search is performed with the ATLAS detector at the Large Hadron Collider using 139 fb(-1) of pp collisions at root s = 13 TeV. The search targets events from ZH production in an NMSSM scenario where H -> chi(similar to 0)(2)chi(similar to 0)(1), with chi(similar to 0)(2) -> a chi(similar to 0)(1), where a is a light pseudoscalar Higgs boson and chi(similar to 0)(1,)(2) are the two lightest neutralinos. The decay of the a boson into a pair of b-quarks results in a peak in the dijet invariant mass distribution. The final-state signature consists of two leptons, two or more jets, at least one of which is identified as originating from a b-quark, and missing transverse momentum. Observations are consistent with Standard Model expectations and upper limits are set on the product of cross section times branching ratio for a three-dimensional scan of the masses of the chi(similar to 0)(2), chi(similar to 0)(1) and a boson.