Municipal solid waste incineration bottom ash (MSWI BA) is the main output of the municipal solid waste incineration process, both in mass and volume. It contains some heavy metals that possess market value, but may also limit the utilization of the material. This study illustrates a robust and simple heap leaching method for recovering zinc and copper from MSWI BA. Moreover, the effect of autotrophic and acidophilic bioleaching microorganisms in the system was studied. Leaching yields for zinc and copper varied between 18–53% and 6–44%, respectively. For intensified copper dissolution, aeration and possibly iron oxidizing bacteria caused clear benefits. The MSWI BA was challenging to treat. The main components, iron and aluminum, dissolved easily and unwantedly, decreasing the quality of pregnant leach solution. Moreover, the physical nature and the extreme heterogeneity of the material caused operative requirements for the heap leaching. Nevertheless, with optimized parameters, heap leaching may offer a proper solution for MSWI BA treatment.