  In this paper we develop a notion of Gibbs measure for the geodesic flow
tangent to a foliated bundle over a compact and negatively curved basis. We
also develop a notion of $F$-harmonic measure and prove that there exists a
natural bijective correspondence between the two.
  For projective foliated bundles with $\mathbb{C}\mathbb{P}^1$-fibers without
transverse invariant measure, we show the uniqueness of these measures for any
H\"older potential on the basis. In that case we also prove that $F$-harmonic
measures are realized as weighted limits of large balls tangent to the leaves
and that their conditional measures on the fibers are limits of weighted
averages on the orbits of the holonomy group.
