The Milky Way bulge is an important tracer of the early formation and chemical enrichment of the Galaxy. The abundances of different iron-peak elements in field bulge stars can give information on the nucleosynthesis processes that took place in the earliest supernovae. Cobalt (Z=27) and copper (Z=29) are particularly interesting.We aim to identify the nucleosynthesis processes responsible for the formation of the iron-peak elements Co and Cu. Methods. We derived abundances of the iron-peak elements cobalt and copper in 56 bulge giants, 13 of which were red clump stars. High-resolution spectra were obtained using FLAMES-UVES at the ESO Very Large Telescope by our group in 2000-2002, which appears to be the highest quality sample of high-resolution data on bulge red giants obtained in the literature to date. Over the years we have derived the abundances of C, N, O, Na, Al, Mg; the iron-group elements Mn and Zn; and neutron-capture elements. In the present work we derive abundances of the iron-peak elements cobalt and copper. We also compute chemodynamical evolution models to interpret the observed behaviour of these elements as a function of iron. The sample stars show mean values of [Co/Fe]~0.0 at all metallicities, and [Cu/Fe]~0.0 for [Fe/H]>-0.8 and decreasing towards lower metallicities with a behaviour of a secondary element. We conclude that [Co/Fe] varies in lockstep with [Fe/H], which indicates that it should be produced in the alpha-rich freezeout mechanism in massive stars. Instead [Cu/Fe] follows the behaviour of a secondary element towards lower metallicities, indicating its production in the weak s-process nucleosynthesis in He-burning and later stages. The chemodynamical models presented here confirm the behaviour of these two elements (i.e. [Co/Fe] vs. [Fe/H]~constant and [Cu/Fe] decreasing with decreasing metallicities).