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In this article, we provide a comprehensive convergence and stability analysis of a semi-Lagrangian scheme for solving nonlinear Burgers' equations with a high-order spatial discretization. The analysis is for the iteration-free semi-Lagrangian scheme comprising the second-order backward finite difference formula (BDF2) for total derivative and the fourth-order central finite difference for diffusion term along the trajectory. The main highlight of the study is to thoroughly analyze the order of convergence of the discrete ℓ2-norm error O(h² +△x4 +△xp+1/h) by managing the relationship between the local truncation errors from each discretization procedure and the interpolation properties with a symmetric high-order discretization of the diffusion term. Furthermore, stability is established by the uniform boundedness of the numerical solution using the discrete Gr¨onwall's Lemma. We provide numerical examples to support the validity of the theoretical convergence and stability analysis for the propounded backward semi-Lagrangian scheme. [ABSTRACT FROM AUTHOR]