In this Monte Carlo study, on a cubic lattice, we examine adsorption and bridging by ABA triblock copolymer chains confined between two parallel flat surfaces. The solvent is assumed to be athermal for both blocks and the only relevant energy parameter is epsilon(AS), the binding energy between the A segments and the surfaces. We study the role of the binding energy and the end block size (N-A) on the fraction of bridging chains. The bridging fraction and the fraction of adsorbing segments both depend explicitly on epsilon(AS) and N-A, and not on the product 2 epsilon(AS)N(A) (which is the maximum available adsorption energy per chain). The dynamic response of the system to step and sinusoidal shear is examined. For N-A = 1, the system essentially behaves as a single Maxwell element. As N-A increases, the stress relaxation becomes increasingly nonexponential with a pronounced tail (due to a spectrum of relaxation times associated with the transient bridging). As for the storage and loss moduli, the limiting slopes (omega --> 0) of log G’ vs log omega G" vs log omega go from 2 to 1 and 1 to 0.5, respectively, as N-A goes from 1 to N-A >> 1.