  A measurement of the inclusive b-jet production cross section is presented in
pp and p-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV, using data collected
with the ALICE detector at the LHC. The jets were reconstructed in the central
rapidity region $|\eta|<0.5$ from charged particles using the anti-$k_{\rm T}$
algorithm with resolution parameter $R=0.4$. Identification of b jets exploits
the long lifetime of b hadrons, using the properties of secondary vertices and
impact parameter distributions. The $p_{\rm T}$-differential inclusive
production cross section of b jets, as well as the corresponding inclusive
b-jet fraction, are reported for pp and p-Pb collisions in the jet transverse
momentum range $10 \le p_{\text{T, ch jet}} \le 100$ GeV/$c$, together with the
nuclear modification factor, $R_{\rm pPb}^{\text{b-jet}}$. The analysis thus
extends the lower $p_{\rm T}$ limit of b-jet measurements at the LHC. The
nuclear modification factor is found to be consistent with unity, indicating
that the production of b jets in p-Pb at $\sqrt{s_{\rm NN}} = 5.02$ TeV is not
affected by cold nuclear matter effects within the current precision. The
measurements are well reproduced by POWHEG NLO pQCD calculations with PYTHIA
fragmentation.
