  We study the asymptotic tail probability of the first-passage time over a
moving boundary for a random walk conditioned to return to zero, where the
increments of the random walk have finite variance. Typically, the asymptotic
tail behavior may be described through a regularly varying function with
exponent -1/2, where the impact of the boundary is captured by the slowly
varying function. Yet, the moving boundary may have a stronger effect when the
tail is considered at a time close to the return point of the random walk
bridge. In the latter case, a phase transition appears in the asymptotics, of
which the precise nature depends on the order of distance between zero and the
moving boundary.
