As a flexible and environmentally friendly technology, bioleaching is widely used to recover base metals from raw materials and industrial waste. This study aimed to test and compare the bioleaching potential of the fungi Aspergillus niger and Penicillium ochrochloron for copper, zinc, and cobalt in a weathered copper slag sample collected from Eliseyna, Bulgaria. Three techniques were employed: direct (one- and two-step) bioleaching of copper slag in the presence of the relevant fungal species, and indirect leaching using spent medium obtained after a week of preliminary fungal cultivation and microbial biomass separation. The results showed that a 5% pulp density was optimal for all bioleaching techniques, with 28 days being the optimal duration for direct techniques and 3 days for indirect techniques. Zinc and cobalt bioleaching efficiencies using A. niger by direct techniques were higher than those using P. ochrochloron, reaching 65.3% and 76.8%, respectively. However, the copper bioleaching efficiency was only 8.3% due to selective precipitation. Significant co-leaching of iron and silicon affected the surface and mineralogy of the copper slag particles. In conclusion, A. niger exhibits higher bioleaching potential for zinc and cobalt in copper slag than P. ochrochloron, with direct and indirect mechanisms playing nearly equal roles in their leaching.