The temporal evolution of photoluminescence in individual single-walled carbon nanotubes (SWNT) under strong laser irradiation is studied and pronounced blinking and bleaching is observed, caused by photoinduced oxidation that subsequently quenches mobile excitons. The nanotubes are isolated with sodium cholate and spun onto either a glass or mica surface. Their bleaching behavior is investigated for variable laser intensities in air and argon atmosphere. The decay rate for luminescence bleaching generally increases with higher laser intensity, however saturating on mica substrates, which is attributed to limited availability of oxygen in the vicinity of the nanotubes. Step-like events in the luminescence time traces corresponding to single oxidation events are analyzed regarding relative step height and suggest an exciton diffusion range of about 105 nm.