Stellar feedback in Galactic bulges plays an essential role in shaping the evolution of galaxies. To quantify this role and facilitate comparisons with X-ray observations, we conduct three-dimensional hydrodynamical simulations with the adaptive mesh refinement code, flash, to investigate the physical properties of hot gas inside a Galactic bulge, similar to that of our Galaxy or M 31. We assume that the dynamical and thermal properties of the hot gas are dominated by mechanical energy input from supernovae (SNe), primarily type Ia, and mass injection from evolved stars as well as iron enrichment from SNe. We study the bulge-wide outflow as well as the SN heating on scales down to ∼4 pc. An embedding scheme that is devised to plant individual supernova remnant (SNR) seeds allows examining, for the first time, the effect of sporadic SNe on the density, temperature and iron ejecta distribution of the hot gas as well as the resultant X-ray morphology and spectrum. We find that the SNe produce a bulge wind with highly filamentary density structures and patchy ejecta. Compared with a one-dimensional (1D) spherical wind model, the non-uniformity of simulated gas density, temperature and metallicity substantially alters the spectral shape and increases the diffuse X-ray luminosity. The differential emission measure as a function of temperature of the simulated gas exhibits a lognormal distribution, with a peak value much lower than that of the corresponding 1D model. The X-ray luminosity depends sensitively on the mass-loss rate from evolved stars. The bulk of the X-ray emission comes from the relatively low-temperature and low-abundance gas shells associated with SN blastwaves. SN ejecta are not well mixed with the ambient medium, at least in the bulge region. These results, at least partly, account for the apparent lack of evidence for iron enrichment in the soft X-ray-emitting gas in Galactic bulges and intermediate-mass elliptical galaxies. The bulge wind helps to explain the ‘missing’ stellar feedback in such galaxies. But the resultant diffuse emission is more than one order of magnitude less than that observed in the Galactic and M 31 bulges, indicating that gas in these bulges is in a subsonic outflow state probably due to additional mass loading to the hot gas and/or due to energy input rate that is substantially lower than the current estimate.