  Any action of a group $\Gamma$ on $\mathbb H^3$ by isometries yields a class
in degree three bounded cohomology by pulling back the volume cocycle to
$\Gamma$. We prove that the bounded cohomology of finitely generated Kleinian
groups without parabolic elements distinguishes the asymptotic geometry of
geometrically infinite ends of hyperbolic $3$-manifolds. That is, if two
homotopy equivalent hyperbolic manifolds with infinite volume and without
parabolic cusps have different geometrically infinite end invariants, then they
define a $2$ dimensional subspace of bounded cohomology. Our techniques apply
to classes of hyperbolic $3$-manifolds that have sufficiently different end
invariants, and we give explicit bases for vector subspaces whose dimension is
uncountable. We also show that these bases are uniformly separated in
pseudo-norm, extending results of Soma. The technical machinery of the Ending
Lamination Theorem allows us to analyze the geometrically infinite ends of
hyperbolic $3$-manifolds with unbounded geometry.
