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TbBaFe₂O_5+δ (TBFO) is a mixed valence compound with antiferromagnetic order (T_N = 450 K) that changes along with the crystal structure and conductivity upon cooling below a Verwey-like transition (T_V = 280 K). This type of double-cell-layered-perovskite is useful to study putative charge ordering in fractional valence systems because the crystal structure develops unique sites for the different valence states. While the static magnetic structure of TBFO is known, in this study we investigate the magnetic interactions. Single crystal inelastic neutron scattering experiments at T = 4 K < T_V and T = 320 K > T_V show spin-waves that are modeled with linear spin wave theory to extract magnetic anisotropy and superexchange parameters. Below T_V there is a sizable magnon gap due to an easy-axis magnetic anisotropy that closes above T_V resulting from the evolution to easy-plane anisotropy. The magnetic interactions are found to be highly three-dimensional and change across T_V. Above T_V, where the conductivity is greater, a damping term is required to model the spin waves.