The interactions between a receptor-modified planar surface and a surface grafted with a bimodal polymer layer, where one of the polymer species is ligand functionalized, are studied using a molecular theory. The effects of changing the binding energy of the ligand-receptor pair, the polymer surface coverage, the composition, and molecular weight of both the unfunctionalized and ligand functionalized polymers on the interactions between the surfaces are investigated. Our findings show that bridging exists between the surfaces including when the molecular weight of the ligand-bearing polymer is smaller than that of the unfunctionalized polymer, even though the ligand is initially buried within the polymer layer. The distance at which the surfaces bind depends only on the molecular weight of the ligand-modified polymer, while the strength of the interaction at a given surface separation can be tuned by changing the molecular weight of the polymers, the total polymer surface coverage, and the fraction of ligated polymers. The composition Of the bimodal layer alters the structure of the polymer layer, thereby influencing the strength of the steric repulsions between the surfaces. Our theoretical results show good agreement with experimental data. The present theoretical study can be used as guidelines for the design of surfaces with tailored abilities for tunning the binding strength and surface-ligand separation distances for polymer-grafted surfaces bearing specific targeting ligands.