We present a measurement of b jet transverse momentum (pt) spectra in proton-lead (pPb) collisions using a dataset corresponding to about 35 inverse nanobarns collected with the CMS detector at the LHC. Jets from b quark fragmentation are found by exploiting the long lifetime of hadrons containing a b quark through tagging methods using distributions of the secondary vertex mass and displacement. Extracted cross sections for b jets are scaled by the effective number of nucleon-nucleon collisions and are compared to a reference obtained from PYTHIA simulations of pp collisions. The PYTHIA-based estimate of the nuclear modification factor is found to be 1.22 +/- 0.15 (stat + syst pPb) +/- 0.27 (syst PYTHIA) averaged over all jets with pt between 55 and 400 GeV/c and with abs(eta[lab]) < 2. We also compare this result to predictions from models using perturbative calculations in quantum chromodynamics.