The influence of the surface step termination on the metal-organic vapor phase epitaxy of GaAs1-yBiy was explored by examining the epitaxial layer growth rate, composition, and morphology characteristics on the offcut and mesa-patterned (001) GaAs substrates. Vicinal surfaces offcut to (111)B with a high density of As terminated steps ('B-steps') increased the GaAs1-yBiy layer growth rate as well as possessed the fastest lateral growth rate on mesa-patterned substrates at a growth temperature of 420 degrees C, indicating that B-steps enhanced the Ga incorporation. With Bi accumulation on the surface, the Ga incorporation rate was reduced by the Bi preferential presence at B-steps blocking the Ga incorporation. Vicinal surfaces offcut to (111)A, which generated Ga-terminated steps ('A-steps') enhanced the Bi incorporation rate during growth at 380 degrees C. This work reveals that the surface step termination plays an important role in the growth of the metastable alloy. Appropriate choices of both the substrate surface-step structure and other growth parameters could lead to an enhanced Bi incorporation.