Bycatch rates are essential to estimating fishery impacts and making management decisions, but data on bycatch are often limited. Tropical tuna purse seine (PS) fisheries catch numerous bycatch species, including vulnerable silky sharks. Even if bycatch proportion is relatively low, impacts on pelagic ecosystems may be important due to the large size of these fisheries. Partial observer coverage of bycatch is a major impediment to assessing impacts. Here we develop a generic Delta modeling approach for predicting catch of four major bycatch species, including silky sharks, in floating object-associated fishing sets of the French Indian Ocean PS fleet from 2011 to 2018 based on logbook and observer data. Cross-validation and variable selection are used to identify optimal models consisting of a random forest model for presence-absence and a negative binomial general-additive model for abundance when present. Though models explain small to moderate amounts of variance (5-15%), they outperform a simpler approach commonly used for reporting, and they allow us to estimate total annual bycatch for the four species with robust estimates of uncertainty. Interestingly, uncertainty relative to mean catch is lower for top predators than forage species, consistent with these species having similar behavior and ecological niches to tunas.