The bridging attraction, mediated by associative, triblock: copolymers with insoluble end blocks and a soluble spacer block, is analyzed using scaling arguments and analytical methods. Adsorbing these associative polymers (APs) onto a single surface, the approach of another, bare, surface results in a strong bridging attraction. When both slit surfaces bear adsorbed APs, the bridging attraction is much weaker. The main contribution is an entropic gain since bridge formation decreases the monomer number density in the crowded region near the surface.