High levels of within-population behavioural variation can have drastic demographic consequences, thus changing the evolutionary fate of populations. A major source of within-population heterogeneity is personality. Nonetheless, it is still relatively rarely accounted for in social learning studies that constitute the most basic process of cultural transmission. Here, we performed in female mosquitofish (Gambusia holbrooki) a social learning experiment in the context of mate choice, a situation called mate copying (MC), and for which there is strong evidence that it can lead to the emergence of persistent traditions of preferring a given male phenotype. When accounting for the global tendency of females to prefer larger males but ignoring differences in personality, we detected no evidence for MC. However, when accounting for the bold–shy dichotomy, we found that bold females did not show any evidence for MC, while shy females showed significant amounts of MC. This illustrates how the presence of variation in personality can hamper our capacity to detect MC. We conclude that MC may be more widespread than we thought because many studies ignored the presence of within-population heterogeneities.