Femtosecond Bessel-Gauss beams are attractive tools to a large area of laser processes including high aspect ratio volume nanostructuration in dielectric materials. Understanding the dielectric material response to femtosecond Bessel-Gauss beam irradiation is key in controlling its modifications and designing new structures. In this work, we show how the material ionization affects the propagation of the femtosecond Bessel-Gauss laser beam and can limit the laser energy deposition. By performing 2D/3D numerical simulations, we evaluate the absorbed laser energy and subsequent material modifications. First, we model the electron dynamics in the material coupled to the 3D laser propagation effects. Then, we consider 2D thermoelasto-plastic simulations to characterize the medium modifications. Results show that the laser ionized matter induces a screening of the incident gaussian beams which form the Bessel-Gauss beam. This effect leads to a limitation of the maximum laser energy deposition even if the incident laser energy increases. It can be reduced if a tigthly focused femtosecond Bessel-Gauss beam is used as the angular aperture of the cone along which the incident gaussian beams are distributed is larger.