This Monte Carlo study investigates telechelic chains, which can adsorb by either end to a surface. They are in an athermal solvent confined between two parallel flat plates, in a regime where the concentration in the polymer layer is at or above the overlap concentration. The chains in the adsorbed layers are not strongly perturbed compared to their free state. In other words, the chains are in the so-called "mushroom" regime. The effects of the separation of the surfaces, L, number of segments in a chain, N, and energetics of the interaction between the chain end and the surface, epsilon/kT, are explored. Of specific interest are (i) the relative populations of elastically inactive chains (free chains, dangling chains, and loops) and elastically active chains (bridges) and (ii) the structure of the adsorbed layers (i.e., the total segment density distributions and the contribution of each conformation to that total). There is a well-defined threshold surface separation, L(t), corresponding roughly to twice the free layer height, 2h, at which bridges first appear. This threshold separation appears to be independent of epsilon/kT in the semidilute regime. The fraction of chains that form bridges, f(b), can be expressed as a function of the dimensionless penetration depth xi/2h is-equal-to (1 - L/L(t)), which does not depend explicitly upon N, i.e., f(b) = f(b)(xi). In the dilute layer limit, the relative populations of different conformations change in the same ratio as the Boltzmann weighting factors accounting only for the energetics of end adsorption.