This work proposes a unified Bézier-based approach for alleviating locking through Assumed Natural Strains (ANS) methods [1,2] within the Isogeometric Analysis (IGA) framework [3] for shell structures. The shells are modeled using only displacement degrees of freedom, and efficiency in nonlinear elastic analysis is achieved through the MIP approach. In ANS-like methods, covariant compatible strains, which are prone to locking when analyzing thin shell structures, are replaced by their corresponding assumed counterparts. In this work, the Bézier operator provides an efficient and elegant way to adapt traditional FEM techniques to IGA, along with the standard ANS method [1] and the Discrete Strain Gap (DSG) method. While the standard ANS method [1] interpolates compatible strains at specific locations (referred to as tying points) and derives assumed strains through element-based extrapolation, the DSG method focuses on calculating modified membrane and shear strain distributions that are free from parasitic components by employing discrete strain gaps. Departing from the original ANS and DSG concepts, we redefine the assumed quadratic matrices (e.g., Q11, Q22, and Q12 responsible for membrane locking, as well as Q13 and Q23 responsible for shear locking) over the Bézier element domain. This variant of the ANSs offers notable benefits, as both the linear and nonlinear components of membrane and shear strains are consistently represented by these matrices without loss of generality. This approach simplifies the evaluation of strain measures and their variations, providing significant advantages for nonlinear analysis. The introduced IGA-ANS techniques effectively mitigate membrane and shear locking, leveraging the superior geometric approximation capabilities of the IGA framework and the high regularity of computer-aided design basis functions. Their effectiveness is demonstrated through extensive numerical testing.