Many properties and applications of single-wall carbon nanotubes (SWCNTs) depend strongly on the coatings that allow their suspension in aqueous media. We report that SWCNT fluorescence is quenched by reversible physisorption of dye molecules such as methylene blue, and that measurements of that quenching can be used to infer structure-specific exposures of the nanotube surface to the surrounding solution. SWCNTs suspended in single-stranded DNA oligomers show quenching dependent on the combination of nanotube structure and ssDNA base sequence. Several sequences are found to give notably high or low surface coverages for specific SWCNT species. These effects seem correlated with the selective recognitions used for DNA-based structural sorting of nanotubes. One notable example is that dye quenching of fluorescence from SWCNTs coated with the (ATT)4 base sequence is far stronger for one (7,5) enantiomer than for the other, showing that coating coverage is associated with the coating affinity difference reported previously for this system. Equilibrium modeling of quenching data has been used to extract parameters for comparative complexation constants and accessible surface areas. Further insights are obtained from molecular dynamics simulations, which give estimated contact areas between ssDNA and SWCNTs that correlate with experimentally inferred surface exposures and account for the enantiomeric discrimination of (ATT)4.