We give bijections between bipolar-oriented (acyclic with unique source and sink) planar maps and certain random walks, which show that the uniformly random bipolar-oriented planar map, decorated by the "peano curve" surrounding the tree of left-most paths to the sink, converges in law with respect to the peanosphere topology to a $4/3$-Liouville quantum gravity surface decorated by an independent Schramm-Loewner evolution with parameter $\kappa =12$ (i.e., SLE$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$). This result is universal in the sense that it holds for bipolar-oriented triangulations, quadrangulations, $k$-angulations, and maps in which face sizes are mixed.