The evolution and the fate of a bubble-perturbed Bartnik-McKinnon (BK) spacetime are investigated. The infinitesimal neighborhood of the origin in a BK spacetime is shown to be equivalent to a part of a Yang-Mills cosmology (YMC) spacetime. If an arbitrarily chosen small region near the origin in the BK spacetime is replaced by a YMC bubble with the same curvature, the YMC-BK system describes a small perturbed BK spacetime. The bubble can expand as a part of the YMC spacetime in the BK spacetime. There is a thin shell between the YMC bubble and the BK spacetime whose trajectory is non-spacelike. The instability of the BK spacetime is described by the evolution of the bubble.