Context. Stars presently identified in the bulge spheroid are probably very old, and their abundances can be interpreted as due to the fast chemical enrichment of the early Galactic bulge. The abundances of the iron-peak elements are important tracers of nucleosynthesis processes, in particular oxygen burning, silicon burning, the weak s-process, and α-rich freeze-out. Aims. The aim of this work is to derive the abundances of V, Cr, Mn, Co, Ni, and Cu in 58 bulge spheroid stars and to compare them with the results of a previous analysis of data from the Apache Point Observatory Galactic Evolution Experiment (APOGEE). Methods. We selected the best lines for V, Cr, Mn, Co, Ni, and Cu located within the H-band of the spectrum, identifying the most suitable ones for abundance determination, and discarding severe blends. Using the stellar physical parameters available for our sample from the DR17 release of the APOGEE project, we derived the individual abundances through spectrum synthesis. We then complemented these measurements with similar results from different bulge field and globular cluster stars, in order to define the trends of the individual elements and compare with the results of chemical-evolution models. Results. We verify that the H-band has useful lines for the derivation of the elements V, Cr, Mn, Co, Ni, and Cu in moderately metalpoor stars. The abundances, plotted together with others from high-resolution spectroscopy of bulge stars, indicate that: V, Cr, and Ni vary in lockstep with Fe; Co tends to vary in lockstep with Fe, but could be showing a slight decrease with decreasing metallicity; and Mn and Cu decrease with decreasing metallicity. These behaviours are well reproduced by chemical-evolution models that adopt literature yields, except for Cu, which appears to drop faster than the models predict for [Fe/H]<‑0.8. Finally, abundance indicators combined with kinematical and dynamical criteria appear to show that our 58 sample stars are likely to have originated in situ.