DNA topoisomerases are enzymes that control DNA topology and are vital targets for antimicrobial and anticancer drugs. Here we present a mass spectrometry study of complexes formed between the A subunit of the topoisomerase DNA gyrase and the bifunctional inhibitor simocyclinone D8 (SD8), an antibiotic isolated from Streptomyces. These studies show that, in an alternative mode of interaction to that found by X-ray crystallography, each subunit binds a single bifunctional inhibitor with separate binding pockets for the two ends of SD8. The gyrase subunits form constitutive dimers, and fractional occupancies of inhibitor-bound states show that there is strong allosteric cooperativity in the binding of two bifunctional ligands to the dimer. We show that the mass spectrometry data can be fitted to a general model of cooperative binding via an extension of the "tight-binding" approach, providing a rigorous determination of the dissociation constants and degree of cooperativity. This general approach will be applicable to other systems with multiple binding sites and highlights mass spectrometry's role as a powerful emerging tool for unraveling the complexities of biomolecular interactions.