  We give a complete list of the cobounded actions of solvable Baumslag-Solitar
groups on hyperbolic metric spaces up to a natural equivalence relation. The
set of equivalence classes carries a natural partial order first introduced by
Abbott-Balasubramanya-Osin, and we describe the resulting poset completely.
There are finitely many equivalence classes of actions, and each equivalence
class contains the action on a point, a tree, or the hyperbolic plane.
