If the gamma-ray excess towards the inner Galaxy (GCE) detected in Fermi-LAT data is due to millisecond pulsars (MSPs), one expects an associated gravitational wave (GW) signal, whose intensity exceeds the disk MSP population emission by an order of magnitude. We compute the expected GW counterpart of the bulge MSP population based on fits of the GCE, and estimate the sensitivity reach of current and future terrestrial GW detectors. The bounds on the average population ellipticity ϵ are competitive with the existing ones derived by LIGO/Virgo towards known MSPs. With a 10-yr data taking in current LIGO/Virgo configuration, one would detect a signal at the level ϵ≃10^{-7}, while ϵ≃10^{-8} would be attainable with a similar data taking period with a third generation GW detector. This sensitivity should be sufficient for crucial diagnostics on the GCE interpretation in terms of MSPs.