Within animal populations, behaviour often varies consistently among individuals, yet it remains unclear what generates and maintains this variation in ‘animal personality’. To understand how multiple sources of variation might combine to promote interindividual differences in behaviour, we examined dispersal behaviour in a colonial spider, Cyrtophora citricola. We measured the repeatability of two behaviours in the laboratory that are associated with dispersal: latency to tiptoe (a dispersal behaviour in spiders) and latency to explore a new environment. We then tested five hypothesized sources of consistent variation across two generations of spiders: sex, food resources, transient internal states, heritability and parental effects. Spiders were modestly consistent in both latency to tiptoe and latency to explore. Males behaved similarly to females of the same size; however, males mature at a smaller size than females, and females became much more hesitant to tiptoe and explore as they grew. Food availability had no effect on either behaviour. Repeatability of exploration was higher within an instar than across instars, suggesting that some aspect of spiders' internal state, other than food, maintained relatively high repeatability over short periods. Tiptoe behaviour was significantly heritable for female relatives, but not for male relatives. For exploratory behaviour, siblings showed significant heritability, while parents and offspring did not, suggesting that early natal environments shared by siblings, rather than genes, might account for their similar behaviour. Finally, although food had no effect on the generation of spiders to which the diet was applied, poorly fed fathers had offspring that tiptoed more readily than well-fed fathers, suggesting paternal effects potentially transmitted through epigenetics. Tiptoe and exploratory behaviours were correlated within individuals, yet the overall modest interindividual variation in these two dispersal behaviours was maintained by disparate effects of different sources of variation.