We have studied the effects of uniaxial compression on the zero-phonon photoluminescence spectrum of excitons bound to bismuth impurities in GaP at liquid-helium temperatures. The quantitative stress dependence is consistent with the exciton being associated primarily with the <100> conduction-band minima. The valley-orbit interaction is shown to lower the energy of the singlet, symmetric valley combination of the exciton, and the valley-orbit splitting is estimated to be 30 meV. The polarization of the emission with uniaxial stress applied to the sample, and the stress dependence of the emission lines, are only qualitatively consistent with the j-j coupling model of the exciton. The deformation potentials Du and Du' for the J=1 state of the exciton are measured to be 0.17 and 0.8 eV, respectively, approximately an order of magnitude smaller than the corresponding free-hole deformation potentials and about one-half those of the J=2 state. The J=2 state is observed to be split by ~0.25 meV into a higher Γ3 and a lower Γ4 level. This splitting, as well as other inconsistencies with the simple model, is attributed in part to the dynamic Jahn-Teller effect.