Sesquiterpene alcohol synthase that catalyzes the formation of the pheromone precursor (Z)-alpha-bisabolene from (2Z,6E)-farnesyl diphosphate. (2Z,6E)-farnesyl diphosphate = (Z)-alpha-bisabolene + diphosphate Binds 2 Mg(2+) ions per subunit. Pheromone biosynthesis. Highly expressed in male epidermal tissue associated with the cuticle of ventral sternites. The Asp-Asp-Xaa-Xaa-Asp/Glu (DDXXD/E) motif is important for the catalytic activity, presumably through binding to Mg(2+). Belongs to the terpene synthase family.