Octupole deformation and the relevant spectroscopic properties of neutron-rich odd-mass barium isotopes are investigated in a theoretical framework based on nuclear density functional theory and the particle-core coupling scheme. The interacting-boson Hamiltonian that describes the octupole-deformed even-even core nucleus, as well as the single-particle energies and occupation probabilities of an unpaired nucleon, are completely determined by microscopic axially symmetric (β2,β3) -deformation constrained self-consistent mean-field calculations for a specific choice of the energy density functional and pairing interaction. A boson-fermion interaction that involves both quadrupole and octupole degrees of freedom is introduced, and their strength parameters are determined to reproduce selected spectroscopic data for the odd-mass nuclei. The model reproduces recent experimental results for both even-even and odd-mass Ba isotopes. In particular, for Ba,147145 our results indicate, in agreement with recent data, that octupole deformation does not determine the structure of the lowest states in the vicinity of the ground state, and only becomes relevant at higher excitation energies.