  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 $\varepsilon$ are competitive with the existing ones
derived by LIGO/Virgo towards known MSPs. With a 10-year data taking in current
LIGO/Virgo configuration, one would detect a signal at the level
$\varepsilon\simeq 10^{-7}$, while $\varepsilon\simeq 10^{-8}$ 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.
