We propose a transition-based bubble parser to perform coordination structure identification and dependency-based syntactic analysis simultaneously. Bubble representations were proposed in the formal linguistics literature decades ago; they enhance dependency trees by encoding coordination boundaries and internal relationships within coordination structures explicitly. In this paper, we introduce a transition system and neural models for parsing these bubble-enhanced structures. Experimental results on the English Penn Treebank and the English GENIA corpus show that our parsers beat previous state-of-the-art approaches on the task of coordination structure prediction, especially for the subset of sentences with complex coordination structures.