<p>In this paper, we investigate the integrability problem of the (2+1)-dimensional bidirectional Sawada-Kotera (bSK) equation. Through analyzing the model, we explore the characteristics of nonlinear dynamics. The Bell polynomial method is one of the most useful tools for studying the integrability of nonlinear evolution equations. Using this method, we derive the Bäcklund transformation, Lax pair, infinite many conservation laws, and nonlinear superposition formula of solutions for the (2+1)-dimensional bSK equation. Then, we constructed the lump-type solutions and soliton solutions of the equation respectively by utilizing its bilinear form and the nonlinear superposition formula of solutions. The dynamic behaviors of the lump-type solutions, lump-kink solutions, and interaction solutions of the model were deduced via the mathematical symbolic computation system Mathematica, the extended three-wave method, and the homo-clinic test method, with the relationship between local waves in physics being elaborated.</p>