The angular dependence of asymmetric magnetization reversal in exchange biased NiO/Ni bilayers was investigated using a vectorial vibrating sample magnetometer. Different angular dependences of the exchange field, coercivity, and asymmetry were obtained by tuning the NiO layer thickness (tNiO). Comparing the experimental data with the theoretical calculations, we found that the asymmetric magnetization reversal of bilayers with larger tNiO was dominated by competing uniaxial and unidirectional anisotropies, and an additional rotatable anisotropy was required in the simulation to correctly describe the magnetization reversal of bilayers with smaller tNiO. The irreversible magnetization switches of a large amount of antiferromagnetic grains in thin NiO layers are responsible for the rotatable anisotropy, which may also significantly affect the shape of the hysteresis loops and the range of angles with symmetric magnetization reversal.