This paper presents a measurement of b-jet production in Pb+Pb and pp collisions at $\sqrt{s_{_\text {NN}}}=5.02$ TeV with the ATLAS detector at the LHC. The measurement uses 260 $\text {pb}^{-1}$ of pp collisions collected in 2017 and 1.4 $\text {nb}^{-1}$ of Pb+Pb collisions collected in 2018. In both collision systems, jets are reconstructed via the anti-$k_{t}$ 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 $\text {nb}^{-1}$ of Pb+Pb collisions collected in 2018 and the same pp collision data as the b-jet measurement. The nuclear modification factor, $R_\text {AA}$, 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 $R_\text {AA}$ to inclusive jet $R_\text {AA}$ is also presented and suggests that the $R_\text {AA}$ 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.