  We study the motion of an electron bubble in the zero temperature limit where
neither phonons nor rotons provide a significant contribution to the drag
exerted on an ion moving within the superfluid. By using the Gross-Clark model,
in which a Gross-Pitaevskii equation for the superfluid wavefunction is coupled
to a Schr\"{o}dinger equation for the electron wavefunction, we study how
vortex nucleation affects the measured drift velocity of the ion. We use
parameters that give realistic values of the ratio of the radius of the bubble
with respect to the healing length in superfluid $^4$He at a pressure of one
bar. By performing fully 3D spatio-temporal simulations of the superfluid
coupled to an electron, that is modelled within an adiabatic approximation and
moving under the influence of an applied electric field, we are able to recover
the key dynamics of the ion-vortex interactions that arise and the subsequent
ion-vortex complexes that can form. Using the numerically computed drift
velocity of the ion as a function of the applied electric field, we determine
the vortex-nucleation limited mobility of the ion to recover values in
reasonable agreement with measured data.
