A search is presented for the decay of the 125 GeV Higgs boson (H) to a pair of new light pseudoscalar bosons (a), followed by the prompt decay of each a boson to a bottom quark-antiquark pair, H -> aa -> b (b) over barb (b) over bar. The analysis is performed using a data sample of proton-proton collisions collected with the CMS detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb(-1). To reduce the background from standard model processes, the search requires the Higgs boson to be produced in association with a leptonically decaying W or Z boson. The analysis probes the production of new light bosons in a 15 < m(a) < 60 GeV mass range. Assuming the standard model predictions for the Higgs boson production cross sections for pp -> WH and ZH, model independent upper limits at 95% confidence level are derived for the branching fraction B(H -> aa -> b (b) over barb (b) over bar). The combined WH and ZH observed upper limit on the branching fraction ranges from 1.10 for m(a) = 20 GeV to 0.36 for m(a) = 60 GeV, complementing other measurements in the mu mu tau tau, tau tau tau tau and bbll (l = mu, tau) channels.