  We present the first detailed computation of the conversion of a bound muon
into an electron mediated by a doubly charged $SU(2)$ singlet scalar. Although
such particles are not too exotic, up to now their contribution to $\mu$-$e$
conversion is unknown. We close this gap by presenting a detailed calculation,
which will allow the reader not only to fully comprehend the discussion but
also to generalise our results to similar cases if needed. We furthermore
compare the predictions, for both the general case and for an example model
featuring a neutrino mass at 2-loop level, to current experimental data and
future sensitivities. We show that, depending on the explicit values of the
couplings as well as on the actual future limits on the branching ratio,
$\mu$-$e$ conversion may potentially yield a lower limit on the doubly charged
singlet scalar mass which is stronger than what could be obtained by colliders.
Our results considerably strengthen the case for low-energy lepton flavour
violation searches being a very valuable addition to collider experiments.
