Amorphous solid dispersions are widely used to enhance the oral bioavailability of poorly water-soluble drugs. Polymeric additives are commonly used to delay crystallization of the drug from the supersaturated solutions formed upon ASD dissolution by influencing the nucleation and growth of crystals. However, there is limited evidence regarding the mechanisms by which polymers stabilize supersaturated drug solutions. The current study used experiments and computational modeling to explore polymer-drug interactions in aqueous solutions. Nucleation induction times for supersaturated solutions of nine drugs in the presence of five newly synthesized cellulose-based polymers were evaluated. The polymers had carboxylic acids substituents with additional variations in the side-chain structure: (1) one with a single side chain and a carboxylic acid termination, (2) three with a branched side chain terminated with a carboxylic and an alcohol group (varying the cellulose linkage and the length of the hydrocarbon side chain), and (3) one with a branched side chain with two carboxylic acid end groups. The polymers with a short side chain and one carboxylic acid were effective, whereas the polymers with the two carboxylic acids or a long hydrocarbon chain were less effective. Atomic force microscopy experiments, evaluating polymer adsorption onto amorphous drug films, indicated that the effective polymers were uniformly spread across the surface. These results were supported by molecular dynamics simulations of a polymer chain in the presence of a drug aggregate in an aqueous environment, whereby the effective materials had a higher probability of establishing close contacts and more negative estimated free energies of interaction. The insights provided by this study provide approaches to design highly effective polymers to improve oral drug delivery.