The concept of animal personality is based on consistent individual differences in behaviour, yet little is known about the factors responsible for such variation. Theory based on sex-specific selection predicts sexual dimorphism in personality-related traits and, in some cases, differences in trait variances between the sexes. In this study, we examined the sources of individual variation for boldness behaviour in guppies (Poecilia reticulata). We first demonstrated heightened boldness expression in males relative to females across feral wild types, artificially selected domestic 'designer' guppies, and putative hybrids of the two. Boldness and body size covaried at the strain level but were not associated among individuals within strains. We also found high and repeatable behavioural differences among individuals (0.40 > intraclass r > 0.60) in all sex/strain groups except hybrid strain females. However, there was no evidence for the heightened inter-individual male variance anticipated for personality traits subject to certain forms of directional sex-specific selection. Domestic fish were boldest overall, and indicated the largest sex difference, which is consistent with genetic linkage between boldness and male ornamental colouration. Consistently high intrinsic variation in boldness behaviour, which extends to inbred domesticated fish, may in part underpin the invasive potential of this species.