The possibility of laser cooling of bismuth hydride (BiH) molecules has been investigated based on high-level ab initio calculations by considering the core-valence and the spin-orbit coupling (SOC) effects. The potential energy curves of the 12 Λ-S states as well as the 25 Ω states that split from them via SOC are obtained by multireference configuration interaction plus the Davidson correction. The properties of b-X transition are investigated. Based on our calculations, we show that the transition between Ω states b0+-X10+ of BiH is a possible candidate for laser cooling, with consideration of the intermediate Ω state X21. An optical cycling scheme is proposed by utilizing four lasers at wavelengths around 471 and 601 nm with 5400 cycles for photon absorption/emission and a sub-microkelvin temperature. Our study should shed some light on searching for possible molecular candidates for laser cooling with the existence of an intermediate electronic state.