  We present several bijections, in terms of combinatorial objects counted by
the Schr\"oder numbers, that are then used (via coloring) for the construction
and enumeration of rational Schr\"oder paths with integer slope, ordered rooted
trees, and simple rooted outerplanar maps. On the other hand, we derive partial
Bell polynomial identities for the little and large Schr\"oder numbers, which
allow us to obtain explicit enumeration formulas.
