Theoretical derivations and numerical calculations of the beam-shape coefficients (BSCs) of the generalized Lorenz-Mie theory (GLMT) are presented by adopting the integral localized approximation and assuming, for the first time in the literature, an arbitrary v-th order Bessel beam. Numerical comparisons between our new approach and other time-consuming methods, such as quadratures, are performed, and it is revealed that the integral localized approximation provides a fast and efficient code for numerically evaluating the BSCs of Bessel beams and their associated electromagnetic field components. This new fast and robust approach can be advantageously used in the analysis of scattering problems with Bessel beams, such as in optical trapping systems.