Optical absorption and transient photobleaching in solutions of surfactant encapsulated and DNA wrapped single-walled carbon nanotubes (SWNTs) are studied. Optical transitions between van Hove singularities are red shifted in solutions of DNA wrapped SWNTs compared with transitions in solutions of sodium dodecyl sulfate (SDS) encapsulated SWNTs. This red shift may be due to changes in the local surrounding dielectric constant and corresponding changes in charge screening. Transient photobleaching at the E11 transition of semiconducting SWNTs is observed in both solutions of SDS encapsulated SWNTs and DNA wrapped SWNTs in response to optical excitation at corresponding E22 transitions, and the saturation of photobleaching at high excitation intensities greater than 500 W cm-2 is studied. It is found that the photobleaching intensity does not saturate as significantly in solutions of DNA wrapped SWNTs as in solutions of SDS isolated SWNTs. Lastly, using degenerate, delayed pump-probe characterization, the temporal relaxation of excited charge carriers is investigated. Measured decays are characterized by both fast and slow processes. The slow decay time constant across the band gap of semiconducting SWNTs is fit to 120 ps for SDS encapsulated SWNTs and 73 ps for DNA wrapped SWNTs.