Engineering wood and bamboo composites bonded by organic adhesives have gradually become an important component in studies of green and sustainable development in the field of civil engineering. As an alternative solution, studies on inorganic adhesives in bio-based composites have sparked widespread research interest. Herein, a novel bamboo-based composite prepared with an inorganic adhesive was proposed, which is named “inorganic-bonded bamboo composite” and abbreviated as InorgBam. The compressive mechanical property is experimentally investigated. Fifteen groups of columns with various slenderness ratios are tested to evaluate the load–bearing capacity and buckling behavior under axial compressive load. The load–lateral deflection curves and stress–strain curves of the InorgBam columns correlated to the slenderness ratios were obtained. Results show that the strength failure with crushing at the end and buckling failure are the two typical failure modes of the InorgBam column under axial compression. The Euler formula and Newlin–Gahagan approach are adopted for calculating the ultimate stress in cases involving strength failure and buckling failure, and the stability coefficient of the InorgBam columns is analyzed using the prediction methods in the existing codes for the design of timber structures. The stability coefficient calculated by using formulas in the current codes for timber structures is feasible for InorgBam columns, and a proposed formula for the stability coefficient in the present study can be finely applied to the design of InorgBam columns. This study has valuable reference in promoting the structural application of this bamboo-based biomaterials.