Essential oils (EOs) from various medicinal and aromatic plants are known for their diverse biological activities, including their antimicrobial effects. Citrus aurantium EO is traditionally used for therapeutic benefits due to its high content of bioactive compounds. Therefore, this study focuses on its potential use as a food preservative by investigating the combined antibacterial properties of EOs from leaves (EO1), flowers (EO2), and small branches (EO3) of Citrus aurantium against six bacterial strains by the agar disk diffusion, minimum inhibitory concentration (MIC), and minimum bactericidal concentration (MBC) methods. The chemical compositions of the EOs were analysed by gas chromatography–mass spectrometry (GC-MS) and revealed the presence of numerous compounds responsible for their antimicrobial properties. The MIC values for the EOs were 3.12 mg/mL, 4.23 mg/mL, and 1.89 mg/mL, for EO1, EO2 and EO3, respectively, while the MBC values were 12.5 mg/mL, 6.25 mg/mL, and 6.25 mg/mL, respectively. A simplex centroid design was created to analyse the effect of the individual and combined EOs against E. coli. The combined EOs showed enhanced antibacterial activity compared to the individual oils, suggesting a synergistic effect (e.g., trial 9 with an MIC of 0.21 mg/mL), allowing the use of lower EO concentrations and reducing potential negative effects on food flavour and aroma. Additionally, the practical application of investigated EOs (at concentrations twice the MIC) was investigated in raw chicken meat stored at 4 °C for 21 days. The EOs, individually and in combination, effectively extended the shelf life of the meat by inhibiting bacterial growth (total bacterial count of less than 1 × 104 CFU/g in the treated samples compared to 7 × 107 CFU/g in the control on day 21 of storage). The study underlines the potential of C. aurantium EOs as natural preservatives that represent a sustainable and effective alternative to synthetic chemicals in food preservation.