Aggregates of conjugated organic molecules (i.e., dyes) may exhibit relatively large one- and two-exciton interaction energies, which has motivated theoretical studies on their potential use in quantum information science (QIS). In practice, one way of realizing large one- and two-exciton interaction energies is by maximizing the transition dipole moment (μ) and difference static dipole moment (Δd) of the constituent dyes. In this work, we characterized the electronic structure and excited-state dynamics of monomers and aggregates of four asymmetric polymethine dyes templated via DNA. Using steady-state and time-resolved absorption and fluorescence spectroscopy along with quantum-chemical calculations, we found the asymmetric polymethine dye monomers exhibited a large μ, an appreciable Δd, and a long excited-state lifetime (τp). We formed dimers of all four dyes and observed that one dye, Dy 754, displayed the strongest propensity for aggregation and exciton delocalization. Motivated by these results, we undertook a more comprehensive survey of Dy 754 dimer and tetramer aggregates using steady-state absorption and circular dichroism spectroscopy. Modeling these spectra revealed an appreciable excitonic hopping parameter (J). Lastly, we used femtosecond transient absorption spectroscopy to characterize τp of the dimer and tetramer, which we observed to be exceedingly short. This work revealed that asymmetric polymethine dyes exhibited μ, Δd, monomer τp, and J values promising for QIS; however, further work is needed to overcome excited-state quenching and achieve long aggregate τp.