The traversal time for tunneling is a measure of the time during which the transmitted particle can be affected by interactions localized in the barrier. The Buttiker-Landauer approach, which estimates this time by imposing an internal clock on the system, has been applied so far for relatively simple one-dimensional models. Here we apply this approach to estimate the traversal time for electron tunneling through a realistic three-dimensional model of a water layer. Observed structure in the energy dependence of times computed reflects the existence of transient tunneling resonances associated with instantaneous water structures.