Wavelength-dependent pump-probe spectroscopy of micelle-suspended single-walled carbon nanotubes reveals two-component dynamics. The slow component (5-20 ps), which has not been observed previously, is resonantly enhanced whenever the pump photon energy coincides with an absorption peak and we attribute it to interband carrier recombination, whereas we interpret the always-present fast component (0.3-1.2 ps) as intraband carrier relaxation in nonresonantly excited nanotubes. The slow component decreases drastically with decreasing pH (or increasing H+ doping), especially in large-diameter tubes. This can be explained as a consequence of the disappearance of absorption peaks at high doping due to the entrance of the Fermi energy into the valence band, i.e., a 1D manifestation of the Burstein-Moss effect.