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 tunneling between metallic regions occurring through potential barriers generated by a nanotube’s contact areas or bundle surfaces. Based on this model and on experimental data, we describe quantitatively the dependencies of the height of these barriers upon bias current and temperature.