Gelation transitions in a colloidal system, where there is a strong reversible attraction between small, soft microgels and large, hard spheres, are systematically investigated. Different from widely studied depletion attraction systems that are also two-component systems, the strong attraction between small solvent and large solute particles introduces bridging attractions between large solute particles. We conclusively demonstrate that the formation of physical gels at the intermediate volume fraction of our bridging attraction system follows more closely with the percolation line that is in stark contrast to what is observed in depletion attraction systems, where the gelation transition is related with the frustrated spinodal separation, not a purely kinetic phenomenon. Our results introduce a different way to control gelation transitions in spherical colloidal systems, and imply that people need to be prudent when generalizing the physical picture of the gelation transitions obtained from systems with different origins of effective attraction as the solvent molecule may play important roles.