We report polarization dependent photoluminescence studies on unintentionally-, Mg-, and Ca-doped β-Ga₂O₃ bulk crystals grown by the Czochralski method. In particular, we observe a wavelength shift of the highest-energy UV emission which is dependent on the pump photon energy and polarization. For 240 nm (5.17 eV) excitation almost no shift of the UV emission is observed between E||b and E||c, while a shift of the UV emission centroid is clearly observed for 266 nm (4.66 eV), a photon energy lying between the band absorption onsets for the two polarizations. These results are consistent with UV emission originating from transitions between conduction band electrons and two differentially-populated self-trapped hole (STH) states. Calcuations based on hybrid and self-interaction-corrected density functional theories further validate that the polarization dependence is consistent with the relative stability of two STHs. This observation implies that the STHs form primarily at the oxygen atoms involved in the original photon absorption event, thus providing the connection between incident polarization and emission wavelength. The data imposes a lower bound on the energy separation between the self-trapped hole states of ~70-160 meV, which is supported by the calculations.