Sequence-selective bis-intercalating dyes exhibit large increases in fluorescence in the presence of specific DNA sequences. This property makes this class of fluorophore of particular importance to biosensing and super-resolution imaging. Here we report ultrafast transient anisotropy measurements of resonance energy transfer (RET) between thiazole orange (TO) molecules in a complex formed between the homodimer TOTO and double-stranded (ds) DNA. Biexponential homo-RET dynamics suggest two subpopulations within the ensemble: 80% intercalated and 20% non-intercalated. Based on the application of the transition density cube method to describe the electronic coupling and Monte Carlo simulations of the TOTO/dsDNA geometry, the dihedral angle between intercalated TO molecules is estimated to be 81° ± 5°, corresponding to a coupling strength of 45 ± 22 cm-1. Dye intercalation with this geometry is found to occur independently of the underlying DNA sequence, despite the known preference of TOTO for the nucleobase sequence CTAG. The non-intercalated subpopulation is inferred to have a mean inter-dye separation distance of 19 Å, corresponding to coupling strengths between 0 and 25 cm-1. This information is important to enable the rational design of energy transfer systems that utilize TOTO as a relay dye. The approach used here is generally applicable to determining the electronic coupling strength and intercalation configuration of other dimeric bis-intercalators.