By the example of single-walled carbon nanotubes (SWCNT) stabilized by sodium deoxycholate in “water + polyvinyl alcohol” medium, the impact of aggregative peculiarities of a stabilizer on the efficacy of dispersing the photoactive agent is investigated. This feature is collated with respect to alternative common anionic surfactants in SWCNT suspensions. The temporal stability of dispersions of the nanocarbon (SWCNT vs carbon black) stabilized by sodium deoxycholate in a medium with controlled viscosity is juxtaposed. The optical power limiting characteristics of these dispersions versus concentration of a polymer dopant (0–3 wt%) is also monitored. In particular, the resistibility of such materials regarding bleaching phenomena in a pulse-periodic regime (pulse repetition rate 10 Hz) of nanosecond laser irradiation (wavelength 532 nm) is addressed. It is demonstrated that optimal concentration of a polymer dopant (≈1.0 wt%) ensures elimination of bleaching with respect to the irradiation conditions studied.