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The production cross sections of B-s(0) and B+ mesons are reported in proton-proton (pp) collisions recorded by the CMS experiment at the CERN LHC with a center-of-mass energy of 5.02 TeV. The data sample corresponds to an integrated luminosity of 302 pb(-1). The cross sections are based on measurements of the B-s(0)-> J/psi(mu(+)mu(-))phi(1020)(K+K-) and B+-> J/psi(mu(+)mu(-))K+ decay channels. Results are presented in the transverse momentum (p(T)) range 7-50 GeV/c and the rapidity interval |y| < 2.4 for the B mesons. The measured p(T)-differential cross sections of B+ and B-s(0) in pp collisions are well described by fixed-order plus next-to-leading logarithm perturbative quantum chromodynamics calculations. Using previous PbPb collision measurements at the same nucleon-nucleon center-of-mass energy, the nuclear modification factors, R-AA, of the B mesons are determined. For p(T)> 10 GeV/c, both mesons are found to be suppressed in PbPb collisions (with R-AA values significantly below unity), with less suppression observed for the Bs0 mesons. In this p(T) range, the R-AA values for the B+ mesons are consistent with those for inclusive charged hadrons and D-0 mesons. Below 10 GeV/c, both B+ and B-s(0) are found to be less suppressed than either inclusive charged hadrons or D-0 mesons, with the B-s(0) R-AA value consistent with unity. The R-AA values found for the B+ and B-s(0) are compared to theoretical calculations, providing constraints on the mechanism of bottom quark energy loss and hadronization in the quark-gluon plasma, the hot and dense matter created in ultrarelativistic heavy ion collisions.