The spin Hall effect and the inverse spin Hall effect are important spin-charge conversion mechanisms. The direct spin Hall effect induces a surface spin accumulation from a transverse charge current due to spin-orbit coupling even in nonmagnetic conductors. However, most detection schemes involve additional interfaces, leading to large scattering in reported data. Here we perform interface-free x-ray spectroscopy measurements at the Cu L_3,2 absorption edges of highly Bi-doped Cu (Cu₉₅Bi₅). The detected x-ray magnetic circular dichroism signal corresponds to an induced magnetic moment of (2.2 ± 0.5) × 10^-12  μ_B A^-1 cm² per Cu atom averaged over the probing depth, which is of the same order of magnitude as found for Pt measured by magneto-optics. The results highlight the importance of interface-free measurements to assess material parameters and the potential of CuBi for spin-charge conversion applications.