As a pure element, bismuth is a semimetal which possesses several interesting physical properties, not all of them well understood. The recent discovery of superconductivity, as predicted by our group, and the increasing superconducting transition temperature as the pressure applied increases, are some examples of its particularities. Also, the fact that the amorphous phase is superconductive with a transition temperature several orders of magnitude larger than the crystalline at ambient pressure is unusual. These phenomena have also motivated our predictions for the transition temperatures of Bi-bilayers and the Bi-IV phase. When mixed with other elements, bismuth seems to contribute to the superconducting character of the resulting material. Here we study the binary copper-bismuth amorphous system which is known to superconduct in diverse compositions. Using ab initio molecular dynamics and the undermelt-quench method, we generate an amorphous structure for a 144-atom supercell corresponding to the Cu61Bi39 system. We calculate the electronic and vibrational densities of states for the amorphous system and estimate a superconducting critical temperature of 4.2 K for the amorphous state.