The extended focal depth of Bessel beams is a very attracting property for glass cutting applications. However, Bessel beam generation with a non-ideal conical lens induces beam pattern distortions. We present our novel results on bulk modifications of soda-lime glass using a non-ideal axicon-generated Bessel beam. Modelling of the Bessel beam pattern and experimental measurements indicated ellipticity of the central core diameter. That resulted in the formation of cracks in a transverse direction inside the bulk of glass. Furthermore, we demonstrate the possibility to control the transverse crack propagation direction, which is crucial in the case of glass cutting applications.