  I prove that every adapted Brownian bridge on a geodesically complete
connected Riemannian manifold is a semimartingale including its terminal time,
without any further assumptions on the geometry. In particular, it follows that
every such process can be horizontally lifted to a smooth principal fiber
bundle with connection, including its terminal time. The proof is based on a
localized Hamilton-type gradient estimate by Arnaudon/Thalmaier.
