An ab initio configuration interaction (CI) study including the spin-orbit coupling interaction is carried out for the lowest 23 states of the bismuth hydride molecule by employing relativistic effective core potentials for the bismuth atom. The computed spectroscopic constants are in good agreement with corresponding experimental data, although there is a tendency to overestimate bond lengths by 0.05-0.10 Angstrom and to underestimate the vibrational frequencies accordingly. The B0(+) excited state is found to have no dissociation barrier, and its radiative lifetime is computed to be 4.3 mu s, with parallel transitions to X(1)0(+) being significantly stronger than the perpendicular B-X(2)1 species. The experimental EO(+) state is assigned as the third root of this symmetry, and its potential curve possesses a dissociation barrier of 1840 cm(-1). This result explains the predissociation characteristics observed for this state and is also consistent with the failure to observe emission from it when attempts are made to form it in recombination processes. This barrier also needs to be taken into account in estimating the X(1)0(+) dissociation energy of this molecule from existing experimental data, and on this basis a D-e value of 2.28 eV is obtained which is in reasonably good agreement with the present directly computed result of 1.98 +/- 0.06 eV. A number of other bound states and avoided crossings are indicated in the calculations which may be of relevance in future experimental investigations of this system.