A search for single production of doubly-charged Higgs bosons has been performed using 600.7~pb$^{-1}$ of $\rm e^+e^-$ collision data with $\sqrt{s}=$~189--209~GeV collected by the OPAL detector at LEP. No evidence for the existence of $\rm H^{\pm\pm}$ is observed. Upper limits on the Yukawa coupling, $\rm h_{ee}$, of the $\rm H^{\pm\pm}$ to like-signed electron pairs are derived. A 95\% confidence level upper limit of $\rm h_{ee}<$~0.08 is inferred for $M({\rm H^{\pm\pm}})<$~160~GeV assuming that the sum of the branching fractions of the $\rm H^{\pm\pm}$ to all lepton flavour combinations is 100\%. Additionally, indirect constraints on $\rm h_{ee}$ from Bhabha scattering, where the $\rm H^{\pm\pm}$ would contribute via $t$-channel exchange, are derived for $M({\rm H^{\pm\pm}})<$~2~TeV. These are the first results for both a single production search and constraints from Bhabha scattering reported from LEP.