Molecular docking (Mol.Doc) techniques were employed to ascertain the binding affinity of two resorcinol-based acridinedione dyes (ADR1 and ADR2) with the widely studied globular protein Bovine Serum Albumin (BSA) in the presence of site-selective binding drugs by Autodock Vina 4.2 software. Docking of various feasible conformers of ADR1 dye with BSA was found to be energetically more favored than ADR2 dye, even though both these dyes differ in the 9th position of the basic dye structure. Analysis of dyes with BSA establishes the location of dye in all of the binding sites of BSA, predominantly through conventional and nonconventional hydrogen-bonding (HB) interactions. The coexistence of hydrophobic interactions resulted in the stability of various conformers generated. The introduction of site I and site II (Sudlow site binding drugs) into ADR1-BSA and ADR2-BSA complexes effectively destabilizes the dye-protein complex; however, the drugs do not displace ADR dyes completely from their selective binding domains. Site II binding drugs effectively destabilize the binding ability of the dye-protein complex rather than site I drugs. However, docking of site I drug 3-carboxyl-4-methyl-5-propyl-2-furanpropanic acid (CMPF) largely destabilizes the ADR1-protein complex, whereas indomethacin (INDO) enhances the binding affinity of the ADR2-protein complex. Interestingly, simultaneous docking of ADR dyes to the BSA-drug complex results in larger stability of the protein-drug complex through HB interactions rather than hydrophobic interactions. Both ADR1 and ADR2 dyes predominantly occupy the Sudlow binding sites of BSA, and the introduction of either site I or site II binding drugs does not displace the dye efficiently from the corresponding binding sites, rather the drugs are effectively displaced toward other binding domains apart from their specific site-binding domains of BSA. Through Mol.Doc techniques, we authenticate that the interactions in host-guest complex systems involving competing ligands are established in depth, wherein the dye as well as the amino acid (AA) moieties in BSA act as both HB donor and acceptor sites apart from several hydrophobic interactions coexisting toward the stability.