Topological insulators demonstrate high charge-spin conversion efficiency due to their spin-momentum locking at the Dirac surface states. However, the surface states are sensitive to disruption caused by exchange coupling when interfaced with a ferromagnet. Here, we demonstrate the use of various nonmagnetic insertion layer materials, Ti, Cu, and Pt, at the Co/Bi-Sb(012) interface to preserve the topological surface state and promote spin-orbit-torque efficiency through the crystallinity control of Bi-Sb(012). For 20-nm-thick Bi-Sb, a spin Hall angle of up to 8.93 is observed with the use of a Pt insertion layer, while it is otherwise negligible for Co/Bi-Sb(012) interfaces. We further explore the enhancement of Bi-Sb(012) crystallinity with increasing Bi-Sb thickness, revealing a rapidly increasing spin-orbit-torque efficiency that gradually saturates above 30 nm. A clear correlation between spin-orbit-torque efficiency and Bi-Sb(012) crystalline size is identified using x-ray diffractometry, establishing the origin of the high spin-orbit efficiency to be the Bi-Sb(012) crystalline orientation. Our work demonstrates the spin-orbittorque origin in Bi-Sb experimentally and paves the way for the adaptation of topological insulators as a class of low-energy spin source material for spintronics applications.