The rate of binding of a grafted polymer to the surface is controlled by entropic barriers. Using a mean-field approximation of ideal polymer dynamics, we first calculate the characteristic binding time for a tethered ligand reaching for a binding site located on the tethering surface. This time is determined by two separate entropic effects: a barrier for the chain to be stretched sufficiently to reach the distant target and a restriction on chain conformations near the surface, versus the increase in available phase space for longer chains. The competition between these two constraints determines the optimal (shortest) binding time. The theory is then extended to model bridging between two surfaces, in particular relevant for cell adhesion. Here the tethered ligand reaches for a receptor on a parallel surface, and the binding time depends on the gap between the two constraining surfaces. Again, an optimal binding time is determined for the given tether geometry. The results look similar to those for free particles in the "narrow escape problem", but modified by an entropic activation factor introduced by the tether.