We investigate experimentally the transport properties of single-walled carbon nanotube bundles as a function of temperature and applied current over broad intervals of these variables. The analysis is performed on arrays of nanotube bundles whose axes are aligned along the direction of the externally supplied bias current. The data are found consistent with a charge transport model governed by the tunnelling between metallic regions occurring through potential barriers generated by nanotubes contact areas or bundles surfaces. Based on this model and on experimental data we describe quantitatively the dependencies of the amplitude of these barriers upon bias current and temperature.