A search for the rare hadronic decay B-s(0) -> p (p) over bar is performed using proton-proton collision data recorded by the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 6 fb(-1). No evidence of the decay is found and an upper limit on its branching fraction is set at B(B-s(0) -> p (p) over bar) < 4.4(5.1)x 10(-9) at 90% (95%) confidence level; this is currently the world's best upper limit. The decay mode B-0 -> p<(p)over bar> is measured with very large significance, confirming the first observation by the LHCb experiment in 2017. The branching fraction is determined to be B(B-0 -> p (p) over bar) = (1.27 +/- 0.15 +/- 0.05 +/- 0.04) 10(-8), where the first uncertainty is statistical, the second is systematic and the third is due to the external branching fraction of the normalization channel B-0 -> K+pi(-). The combination of the two LHCb measurements of the B-0 -> p (p) over bar branching fraction yields B(B-0 -> p (p) over bar) (1.27 +/- 0.13 +/- 0.05 +/- 0.03) x 10(-8).