  In this paper we complete the $\mathrm{ADE}$-like classification of simple
transitive $2$-representations of Soergel bimodules in finite dihedral type,
under the assumption of gradeability. In particular, we use bipartite graphs
and zigzag algebras of $\mathrm{ADE}$ type to give an explicit construction of
a graded (non-strict) version of all these $2$-representations.
  Moreover, we give simple combinatorial criteria for when two such
$2$-representations are equivalent and for when their Grothendieck groups give
rise to isomorphic representations.
  Finally, our construction also gives a large class of simple transitive
$2$-representations in infinite dihedral type for general bipartite graphs.
