Biomass–fungi composite materials primarily consist of biomass particles (sourced from agricultural residues) and a network of fungal hyphae that bind the biomass particles together. These materials have potential applications across diverse industries, such as packaging, furniture, and construction. 3D printing offers a new approach to manufacturing parts using biomass–fungi composite materials, as an alternative to traditional molding-based methods. However, there are challenges in producing parts with desired quality (for example, geometric accuracy after printing and height shrinkage several days after printing) by using 3D printing-based methods. This paper introduces an innovative approach to enhance part quality by incorporating ionic crosslinking into the 3D printing-based methods. While ionic crosslinking has been explored in hydrogel-based bioprinting, its application in biomass–fungi composite materials has not been reported. Using sodium alginate (SA) as the hydrogel and calcium chloride as the crosslinking agent, this paper investigates their effects on quality (geometric accuracy and height shrinkage) of 3D printed samples and physiochemical characteristics (rheological, chemical, and texture properties) of biomass–fungi composite materials. Results show that increasing SA concentration led to significant improvements in both geometric accuracy and height shrinkage of 3D printed samples. Moreover, crosslinking exposure significantly enhanced hardness of the biomass–fungi mixture samples prepared for texture profile analysis, while the inclusion of SA notably improved cohesiveness and springiness of the biomass–fungi mixture samples. Furthermore, Fourier transform infrared spectroscopy confirms the occurrence of ionic crosslinking within 3D printed samples. Results from this study can be used as a reference for developing new biomass–fungi mixtures for 3D printing in the future.