The fine structure of high-L n = 19 and 20 Rydberg states of Ba + has been measured precisely using the resonant excitation Stark ionization spectroscopy technique, allowing for a determination of the Ba 2+ polarizability: α D (Ba 2+ ) = 10.75(10) a.u. This result, in combination with an improved model of the K splittings in Ba Rydberg levels, allows for a more precise determination of the Ba + dipole transition strengths connecting the 6 2 S 1/2 ground state to the 6 2 P 1/2 and 6 2 P 3/2 excited states. The results, in atomic units, are 6 2 S 1/2 ||D|| 6 2 P 1/2 = 3.3251(21) and 6 2 S 1/2 ||D|| 6 2 P 3/2 = 4.7017(27).