This paper presents a measurement of b-jet production in Pb+Pb and pp collisions at sNN=5.02 TeV with the ATLAS detector at the LHC. The measurement uses 260 pb - 1 of pp collisions collected in 2017 and 1.4 nb - 1 of Pb+Pb collisions collected in 2018. In both collision systems, jets are reconstructed via the anti- kt algorithm. The b-jets are identified from a sample of jets containing muons from the semileptonic decay of b-quarks using template fits of the muon momentum relative to the jet axis. In pp collisions, b-jets are reconstructed for radius parameters R= 0.2 and R= 0.4 , and only R= 0.2 jets are used in Pb+Pb collisions. For comparison, inclusive R= 0.2 jets are also measured using 1.7 nb - 1 of Pb+Pb collisions collected in 2018 and the same pp collision data as the b-jet measurement. The nuclear modification factor, RAA , is calculated for both b-jets and inclusive jets with R= 0.2 over the transverse momentum range of 80–290 GeV. The nuclear modification factor for b-jets decreases from peripheral to central collisions. The ratio of the b-jet RAA to inclusive jet RAA is also presented and suggests that the RAA for b-jets is larger than that for inclusive jets in central Pb+Pb collisions. The measurements are compared with theoretical calculations and suggest a role for mass and colour-charge effects in partonic energy loss in heavy-ion collisions.