This study presents numerical simulations of the shallow water equations (SWEs) for the Bay of Bengal (BoB) using the Lagrange–Galerkin method (LGM) on a triangular mesh, with the transmission boundary conditions (TBCs). To examine the positional sensitivity of the transmission boundaries, the simulations are conducted with TBCs imposed at two distinct locations within the Bay of Bengal domain. The computed total mass and -norm of the surface elevation demonstrate that the transmission boundary condition performs efficiently and exhibits minimal dependence on its placement. These results indicate that the TBC is well-suited for modeling open-sea boundaries, ensuring smooth wave propagation without artificial reflection. The study serves as a foundational step toward developing an accurate and stable storm surge prediction framework for the Bay of Bengal using the Lagrange–Galerkin approach.