We explore a scheme for guiding cold atoms through a hollow Bessel beam generated by a single axicon and a lens from a 2D magneto-optical trap toward a science chamber. We compare the Bessel beam profiles measured along the optical axis to a numerical propagation of the beam's wavefront, and we show how it is affected by diffraction during the passage through a long narrow funnel serving as a differential pumping tube between the chambers. We derive an approximate analytic expression for the intensity distribution of the Bessel beam and the dipolar optical force acting on the atoms. By a Monte-Carlo simulation based on a stochastic Runge-Kutta algorithm of the motion of atoms initially prepared at a given temperature we show that a considerable enhancement of the transfer efficiency can be expected in the presence of a sufficiently intense Bessel beam.