If the mysterious Fermi-LAT GeV gamma-ray excess is due to an unresolved population of millisecond pulsars (MSP) in the Galactic bulge, one expects this very same population to shine in X rays. For the first time, we address the question of what is the sensitivity of current X-ray telescopes to an MSP population in the Galactic bulge. To this end, we create a synthetic population of Galactic MSPs, building on an empirical connection between gamma- and X-ray MSP emission based on observed source properties. We compare our model with compact sources in the latest Chandra source catalog, applying selections based on spectral observables and optical astrometry with Gaia. We find a significant number of Chandra sources in the region of interest to be consistent with being bulge MSPs that are as yet unidentified. This motivates dedicated multi-wavelength searches for bulge MSPs: Some promising directions are briefly discussed.