Invariant metrics of positive Ricci curvature on principal bundles

Let Y be a compact connected Riemannian manifold with a metric of positive Ricci curvature.  Let ¥ð : P ¡æ Y be a principal bundle over Y with compact connected structure group G.  If the fundamental group of P is finite, we show that P admits a G invariant metric with positive Ricci curvature so that ¥ð is a Riemannian submersion.