Lattice Monte Carlo simulations are used to analyze a single polymer chain in good solvent confined between two adsorbing walls. Results are reported for the number and size distribution of bridge conformations and the resultant attractive force between the surfaces as a function of intersurface distance, H, and the effective adsorption energy, epsilon, between the polymer segment and the wall. The results are consistent with indirect experimental measurements of bridging in a multichain system and additionally yield information on the mechanism of bridging. In the case of single chains and strong adsorption (epsilon > 0.5 k(B)T), the force per bridge f(br) is independent of separation and depends only on the adsorption energy, in agreement with scaling analysis. In the case of weak adsorption (or for multichain systems) it is explicitly shown that steric interactions (loop-loop, loop-bridge interactions, etc.) are important. The "force per bridge" again has a roughly constant magnitude (appropriately diminished by steric interactions) but cannot be related unequivocally to the adsorption energy at the surface.