The production of B+, B0 and Λb0 hadrons is studied in proton-lead collisions at a center-of-mass energy per nucleon pair of sNN=8.16 TeV recorded with the LHCb detector at the LHC. The measurement uses a dataset corresponding to an integrated luminosity of 12.2±0.3 nb-1 for the case where the proton beam is projected into the LHCb detector (corresponding to measuring hadron production at positive rapidity) and 18.6±0.5 nb-1 for the lead beam projected into the LHCb detector (corresponding to measuring hadron production at negative rapidity). Double-differential cross sections are measured and used to determine forward-backward ratios and nuclear modification factors, which directly probe nuclear effects in the production of beauty hadrons. The double-differential cross sections are measured as a function of the beauty-hadron transverse momentum and rapidity in the nucleon-nucleon center-of-mass frame. Forward-to-backward cross section ratios and nuclear modification factors indicate a significant nuclear suppression at positive rapidity. The ratio of Λb0 over B0 production cross sections is reported and is consistent with the corresponding measurement in pp collisions.