The growing number of drug-resistant pathogenic bacteria poses a global threat to human health. For this reason, the search for ways to enhance the antibacterial activity of existing antibiotics is now an urgent medical task. The aim of this study was to develop novel delivery systems for polymyxins to improve their antimicrobial properties against various infections. For this, hybrid core–shell nanoparticles, consisting of silver core and a poly(glutamic acid) shell capable of polymyxin binding, were developed and carefully investigated. Characterization of the hybrid nanoparticles revealed a hydrodynamic diameter of approximately 100 nm and a negative electrokinetic potential. The nanoparticles demonstrated a lack of cytotoxicity, a low uptake by macrophages, and their own antimicrobial activity. Drug loading and loading efficacy were determined for both polymyxin B and E, and the maximal loaded value with an appropriate size of the delivery systems was 450 µg/mg of nanoparticles. Composite materials based on agarose hydrogel were prepared, containing both the loaded hybrid systems and free antibiotics. The features of polymyxin release from the hybrid nanoparticles and the composite materials were studied, and the mechanisms of release were analyzed using different theoretical models. The antibacterial activity against Pseudomonas aeruginosa was evaluated for both the polymyxin hybrid and the composite delivery systems. All tested samples inhibited bacterial growth. The minimal inhibitory concentrations of the polymyxin B hybrid delivery system demonstrated a synergistic effect when compared with either the antibiotic or the silver nanoparticles alone.