The structure, composition, and function of natural bone have long been the focus of bone tissue engineering. However, existing organic–inorganic 3D printing systems are limited by hydrogel stability and inorganic salt content, hindering the fabrication of robust three-dimensional scaffolds. In this study, we developed a hydrogel–inorganic particle bioink and implemented a multi-step crosslinking strategy. The organic phase, composed of sodium alginate, gelatin, and chitosan, was combined with β-tricalcium phosphate and crosslinked via ionic pre-crosslinking followed by Schiff base reaction to form a dual-crosslinked network. The resulting scaffolds exhibited excellent mechanical properties and biomimetic microarchitecture while maintaining shape stability under physiological conditions. Furthermore, the tunable swelling behavior of the hydrogel enabled efficient loading and controlled release of the small molecule EGCG. This composite scaffold demonstrated adjustable swelling, controllable degradation, and significantly enhanced cellular compatibility, providing a novel, efficient, and scalable strategy for the repair of complex bone defects and offering new insights for the design and application of 3D-printed bone scaffolds.