Single-walled carbon nanotubes (SWCNTs) exhibit excellent nonlinear optical (NLO) properties due to the delocalized π electron states present along their tube axis. Using the open aperture Z-scan method in tandem with X-ray photoelectron spectroscopy (XPS) and Raman spectroscopy, we demonstrate the simultaneous tailoring of both electronic and NLO properties of SWCNTs, from ultrafast (femtosecond) to relatively slow (nanosecond) timescales, by doping with a single substituent, viz., boron. SWCNTs were doped via a wet chemical method using B2O3, and the boron content and bonding configurations were identified using XPS. While in the ns excitation regime, the nonlinear absorption was found to increase with increasing boron concentration in the SWCNTs (due to the increasing disorder and enhanced metallicity of the SWCNTs), the saturation intensity in the fs excitation regime decreased. We attribute this counter-intuitive behavior to excited state absorption on ns timescales, and saturable absorption combined with weak two-photon transitions on fs timescales between van Hove singularities.