Since 2011, the mean number of bites per year by bull sharks Carcharhinus leucas has increased markedly at Réunion Island. To predict areas and periods of increased risk, we need to better understand the space-use dynamics of individual sharks. In coastal waters off Réunion Island, two bull sharks, one of each sex, were double-tagged and tracked for 174 days (male) and 139 days (female) using pop-up satellite archival tags (PSATs) and acoustic transmitters. Both sharks spent most of their time inshore (58.1% for the male and 89.9% for the female). The female performed short excursions but typically remained inshore. The male alternated between spending residence time along the coast and undertaking wide-ranging movements, including one extensive open-ocean excursion to the vicinity of a seamount situated about 210 km from the island. Differences in the residency and home range between the two sharks probably reflect different patterns of foraging and mating behaviours. Our results highlight the advantages of double-tagging in telemetry studies that attempt to estimate the degree of habitat fidelity of a species and illustrate the need to consider the movement patterns of sharks at different scales when developing efficient risk-mitigation management.