Theories of color in cyanine dyes have evolved around the idea of a "resonance" of structures with distinct bonding and charge localization. Understanding the emergence of resonance models from the underlying many-electron problem remains a central issue for these systems. Here, the issue is addressed using a maximum-entropy approach to valence-bond representations of state-averaged complete-active space self consistent field models. The approach allows calculation of energies and couplings of high-energy valence bond structures that mediate superexchange couplings and chemical bonding. A series of valence-bond Hamiltonians for a series of bridge-substituted derivatives of Michler's hydrol blue (a monomethine cyanine) is presented. The Hamiltonians are approximated with a simple linear model parametrized by the Brown Okamoto sigma(+)(p) parameter of the bridge substituent. A quantitative lower bound on sigma(+)(p), beyond which a resonant cyanine-like ground state will not exist, is presented. The large effective coupling in two-state resonance models emerges from superexchange associated with either covalent bonding or charge-carrier delocalization, with the former contribution significantly the stronger. The results provide ab initio justification for empirical diabatic-state models of methine optical response. They are of general interest for understanding the optoelectronic response in cyanines.