Hyperbranched polyglycerol (HPG) is a water-soluble polymer with excellent biocompatibility and holds promising application prospects in various fields. However, the facile preparation of HPG with specific functionalities remains a significant challenge. In this paper, the use of the natural small molecule salicylic acid (SA) simultaneously as initiator core and catalyst to synthesize water-soluble, multifunctional SA-HPG via one-step cationic ring-opening polymerization was reported. The synthesis process requires no organic solvents or metal catalysts, offering a simple, green, and environmentally friendly approach. The cytotoxicity of SA-HPG was evaluated through the thiazolyl blue tetrazolium bromide (MTT) method, and the results indicate good biocompatibility. Antibacterial tests confirm its high antibacterial activity. By blending SA-HPG with an aqueous polyvinyl alcohol (PVA) solution and subsequent film formation, PVA/SA-HPG composite films with significantly enhanced comprehensive properties can be readily prepared. When the mass fraction of SA-HPG is 10%, the composite film exhibits significantly reduced ultraviolet (UV) transmittance while retaining a visible light transmittance of 86%. Its thermal stability is enhanced by 6 °C, and its tensile strength and elongation at break reach 48.6 MPa and 230.0%, respectively, which significantly outperforms those of the pure PVA film.