Closed Virtual Bundle Conjecture for hyperbolic 3-manifolds

Let $M$ be a closed, connected, ${\mathbf{P}^2}$-irreducible $3$-manifold with infinite fundamental group. Closed Virtual Bundle Conjecture. If $M$ is hyperbolic, then some finite-sheeted covering space of $M$ is a surface bundle over $S^1$. This is the virtual fibering assertion paired with the hyperbolization conjecture in the source; the source gives no resolution.