Skin wound repair, a highly integrated and overlapping complex process, is susceptible to infection, excessive inflammation, high oxidative stress, which can prolong the wound healing time or even lead to chronic wound. Meanwhile, single-layer hydrogels are unavoidably dehydrated usually due to water evaporation, which is not conducive to wound healing. Therefore, a bilayer hydrogel dressing composed of gelatin (G) and sodium alginate (A) loaded with ciprofloxacin (C) and curcumin (Cur) was manufactured by extrusion 3D bioprinting technology in this study, which is denoted as GACCur. The experimental results showed that the bilayer hydrogel loaded with 50 µg/mL of Cur (GACCur50) had excellent antibacterial properties and high antioxidative activity with a 54.35 ± 0.48% DPPH scavenging ratio. In addition, this GACCur50 bilayer hydrogel exhibited the capacity to mitigate the polarization of inflammatory cells toward pro-inflammatory states, observably reducing the expression of pertinent pro-inflammatory cytokines. Furthermore, the bilayer hydrogel dressing also showed good biocompatibility as assessed by live-dead fluorescent staining, scanning electron microscopy (SEM), and CCK-8 test. Therefore, the GACCur50 bilayer hydrogel dressing is promising for wound healing.