This paper presents an innovative modular steel channel–concrete composite floor system designed for rapid assembly. This system, compared to traditional steel–concrete composite floors, connects adjacent modules solely through the use of high-strength bolts. This design eliminates the need for on-site wet construction, thereby yielding superior economic benefits. To investigate the proposed system’s mechanical behavior, bending tests were conducted on four composite floors with various support conditions, the numbers of bolts, and the degrees of shear connection. The load–displacement responses, torsional behavior of the channel beams, interfacial slip, and strain development of the composite floor systems were analyzed. The test results show that the simply supported composite floor, without bolted connections, undergoes flexural failure. In contrast, the semi-continuous composite floors, with bolted connections, display punching shear-flexural failure. The pre-tension forces applied to the bolts can effectively mitigate the torsional deformation of the channels and module separation, ensuring that the system maintains excellent structural integrity, sufficient load-bearing capacity, and adequate ductility. The semi-continuous composite floors, when fitted with high-strength bolts, demonstrate an increase in ultimate load-bearing capacity by 13–15%. However, there is a corresponding decrease in ductility by 18–23% when compared to the simply supported composite floor without bolts. The use of perforated steel plates as shear connectors offers efficient shear resistance between the steel channels and concrete slabs, facilitating full composite action of the system throughout the loading process. The paper concludes with the development of a model that calculates the flexural strength and punching shear strength of the composite floors based on the yield-line theory.