The integration of the feeder system in a tokamak involves complex engineering, manufacturing and logistics issues. Therefore, within the pre-conceptual design activities of the European DEMO fusion reactor, it is important to provide a preliminary sizing of the feeders at an early stage. Here we present the conceptual design of superconducting bus bars and current leads for the DEMO feeder system. The proposal is based on three main components: Nb3Sn lead extensions, NbTi bus bars and HTS current leads. We propose three different bus bar designs - for the TF, CS and PF coil feeders, respectively. Two additional values of the TF operating current are considered. The structural verification of the bus bars, including an S-bend geometry for reducing the mechanical loads due to cool down, is performed both analytically and by means of 3D finite-element simulations. In addition, we present an outline design of the HTS current leads, based on the minimisation of the cryogenic heat load and the simulation of a loss-of-flow accident. Finally, we briefly discuss the main characteristics of the joints, as well as some integration and assembly challenges.