A relativistic CI treatment including spin-orbit coupling has been carried out for the low-lying electronic states of bismuth iodide, employing effective core potentials for both atoms. The X(3) Sigma(-) ground state is computed to have a zero-field splitting of 5096 cm(-1), 1086 cm(-1) less than the most recent measured value. The a (1) Delta state is predicted to have a T-e value of 12336 cm(-1), and it is suggested on the basis of correlation effects that the true value should lie about 1000 cm(-1) lower. This conclusion is also based in part on the finding that the computed BO+ T-e value of 24148 cm(-1) overestimates the measured result by 759 cm(-1). The latter state is shown to arise from an avoided crossing between the (1) Sigma(+) and (5) Pi Lambda-S states, which produces only a relatively shallow well and a slight barrier to dissociation. Because the 3 Pi state is repulsive, no other low-lying Omega = 0(+) state is found in the spectrum, similarly as in SbI but in contrast to BiF. Due to the much greater spin-orbit effects in BiI, the composition of the lowest two excited 0(+) states in terms of (1) Sigma(+) and (3) Pi Lambda-S states is notably different than in SbI and this fact is important in understanding why the T-e value of the lowest bound 0(+) states of these two systems are so different. Transition probabilities have also been computed for various pairs of vibrational states. The radiative lifetime of the X(2)1 fine structure component is calculated to be 20.7 ms, which agrees well with a recent measured value of 20 +/- 4 ms by Fink and Shestakov. In agreement with Colin et al.'s empirical rule, it is found that the b-X(2) transition is stronger than b-X(1), and this result also confirms an earlier theoretical analysis of this general phenomenon given by the authors.