We show a lower bound for the boundary crossing probability P{there exists z is an element of [0, 1] : h(z) + B-0(z) > u(z)} with B-0 a Brownian bridge, h a trend function and u a boundary function. By that we get also a lower bound for the boundary crossing probability P{there exists z is an element of [0, 1] : h(z) + B-0(z) < u(z)}. It turns out that the bound improves the asymptotic result given in Bischoff et al. [2003a. Methodology Comput. Appl. Probab. 5 (3), 271-287] when considering a trend function gamma h, gamma -> infinity. The usual tools to obtain boundary crossing probabilities are finite dimensional approximations of the above probability. In this paper, however, we use the Cameron-Martin-Girsanov formula to obtain a bound of the above probability.