We build and apply an textitab initio stochastic Bethe-Salpeter Equation (sBSE) approach to planar cyanine dye aggregate clusters containing up to 2,856 valence electrons. Using a transferable, parameterized screened exchange kernel, we resolve dielectric response, exciton delocalization, and optical spectra within a unified many-body framework. Remarkably, the sBSE transition densities validate the Frenkel exciton picture in real space and provide a practical first-principles route to its screened couplings. The calculations reproduce textitH-, textitI-, and textitJ-like spectral evolution and reveal that spatially dependent screening does not merely shift excitonic bands, but reshapes their dispersion, leading to changes in the relative energies of bright and dark exciton states. These results establish sBSE as a predictive framework for large molecular aggregates.