The nucleation of bubble domains in homeotropic samples of a dielectrically positive cholesteric liquid crystal is described. These domains are found to be more stable in an electric field than the rectilinear double-twisted fingers. The electric field-induced transformation of a looped finger into a bubble domain is described in detail: it is discontinuous and irreversible, and operates only at a large enough confinement ratioC=d/p, wheredis the sample thickness andpthe quiescent cholesteric pitch. Finally, in contrast with Stieb's model [4], we propose that there are two point defects along the bubble axis and not a disclination line.