The efficiency of thin-film organic photovoltaic (OPV) devices relies heavily upon the transport of excitons to type-II heterojunction interfaces, where there is sufficient driving force for exciton dissociation and ultimately the formation of charge carriers. Semiconducting single-walled carbon nanotubes (SWCNTs) are strong near-infrared absorbers that form type-II heterojunctions with fullerenes such as C60. Although the efficiencies of SWCNT-fullerene OPV devices have climbed over the past few years, questions remain regarding the fundamental factors that currently limit their performance. In this study, we determine the exciton diffusion length in the C60 layer of SWCNT-C60 bilayer active layers using femtosecond transient absorption measurements. We demonstrate that hole transfer from photoexcited C60 molecules to SWCNTs can be tracked by the growth of narrow spectroscopic signatures of holes in the SWCNT "reporter layer". In bilayers with thick C60 layers, the SWCNT charge-related signatures display a slow rise over hundreds of picoseconds, reflecting exciton diffusion through the C60 layer to the interface. A model based on exciton diffusion with a Beer-Lambert excitation profile, as well as Monte Carlo simulations, gives the best fit to the data as a function of C60 layer thickness using an exciton diffusion length of approximately 5 nm.