The abundance of organic carbon (OC) in vegetation and soils (~2,600 PgC) compared to carbon in the atmosphere (~830 PgC) highlights the importance of terrestrial OC in global carbon budgets. The residence time of OC in continental reservoirs, which sets the rates of carbon exchange between land and atmosphere, represents a key uncertainty in global carbon cycle dynamics. Retention of terrestrial OC can also distort bulk OC- and biomarker-based paleorecords, yet continental storage timescales remain poorly quantified. Using "bomb" radiocarbon (14C) from thermonuclear weapons testing as a tracer, we model leaf-wax fatty acid and bulk OC 14C signatures in a river-proximal marine sediment core from the Bay of Bengal in order to constrain OC storage timescales within the Ganges-Brahmaputra (G-B) watershed. Our model shows that 79-83% of the leaf-waxes in this core were stored in continental reservoirs for an average of 1,000-1,200 calendar years, while the remainder was stored for an average of 15 years. This age structure distorts high-resolution organic paleorecords across geologically rapid events, highlighting that compound-specific proxy approaches must consider storage timescales. Furthermore, these results show that future environmental change could destabilize large stores of old - yet reactive - OC currently stored in tropical basins.