3D bioprinting uses bioink deposited directly on a collector to create any previously designed 3D model. One of the most common and the easiest to operate bioinks is gelatin–alginate hydrogel. The present study aimed to combine 3D bioprinting with different cross-linking techniques to develop a new stable and biodegradable gelatin–alginate hydrogel matrix for drug delivery applications. The matrix-building biopolymers were crosslinked by ionotropic gelation with Ca2+ ions, chemical crosslinking with GTA or a combination of the two crosslinkers at various concentrations. The influence of the crosslinking method on the hydrogel properties, stability and structure was examined using scanning electron and optical microscopy, differential scanning calorimetry and thermogravimetric analysis. Analyses included tests of hydrogel equilibrium swelling ratio and release of marker substance. Subsequently, biological properties of the matrices loaded with the antibiotic chlorhexidine were studied, including cytotoxicity on HaCAT cells and antibacterial activity on Staphylococcus aureus and Escherichia coli bacteria. The conducted study confirmed that the 3D bioprinted cross-linked drug-loaded alginate–gelatin hydrogel is a good and satisfying material for potential use as a drug delivery system