We measure and analyze the isotope shifts in the multiplet of transitions between the metastable a5F and excited y5Go terms of neutral titanium by probing a titanium vapor in a hollow cathode lamp using saturated absorption spectroscopy. We resolve the five J→J+1 and the four J→J transitions within the multiplet for each of the three I=0 stable isotopes (Ti46, Ti48, and Ti50). The isotope shifts on these transitions allow us to determine the isotope-dependent variation in the fine-structure splitting of the a5F and y5Go levels themselves. Combined with existing knowledge of the nuclear charge radii of titanium nuclei, we derive the specific mass and field shifts, which arise from correlated electronic motion and electronic density at the nucleus respectively, and further observe a strong J-dependent variation in each. Our results yield insight into the electronic and nuclear structure of transition metal atoms like titanium and also characterize optical transitions that may allow for optical manipulation of ultracold gases of transition-metal species.