Cardiovascular diseases represent a worldwide social and economic challenge, due to heart tissue limited regenerative capabilities. 3D bioprinted cell-laden constructs are a promising approach to develop patches for cardiac regeneration or in vitro models for new drug preclinical discovery and validation. However, the development of bioinks with optimal mechanical, rheological, and biological properties is still a challenge. Although alginate (Alg)-based bioinks have been extensively explored, such hydrogels lack cell adhesion properties and degradability. Additionally, 3D Alg structures are usually obtained by micro-extrusion bioprinting exploiting conventional external cross-linking methods, which introduce inhomogeneities and unpredictability in construct formation. This work exploits Alg internal ionic gelation mechanism to obtain homogeneous self-standing multilayered 3D printed constructs without employing support baths or post-printing crosslinking treatments, combining an insoluble calcium salt (calcium carbonate, CaCO₃) with an acidifying agent (D-(+)-Glucono-1,5-lactone, GDL) to promote controlled release of calcium ions. Alg was blended with oxidized alginate (ADA) and gelatin (Gel) to achieve degradable and cell adhesive hydrogels for cardiac tissue engineering. Firstly, ADA/Alg bioink composition was tailored by varying polymer weight ratio (keeping ADA as the main component) and calcium ions concentration to achieve cardiac tissue-like viscoelastic properties. Then, the amount of Gel in ADA/Alg hydrogels was optimized to support adult human cardiac fibroblasts (AHCFs) adhesion, producing shear thinning inks with tunable viscoelastic properties (G’ 650-1300 Pa) and degradation profile (40-80% weight loss after 21 days in phosphate buffered saline, PBS) by varying Gel concentration. ADA/Alg/Gel hydrogels showed a shear thinning behavior suitable for 3D bioprinting and dependent on ink stabilization time, due to the gradual pH-triggered release of calcium ions over time. AHCFs-laden ADA/Alg/Gel bioinks could be successfully printed producing scaffolds with high shape fidelity and good cell viability post-printing. Finally, 3D AHCF-laden and H9C2-laden ADA/Alg/Gel bioinks with the highest gelatin content (25% w/w) allowed cell adhesion after 24 hours of incubation, showing potential application for cardiac tissue modelling. This research presented a comprehensive framework for advancing the design of bioink formulations enabling the printing of cell-adhesive and self-supporting constructs.