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A bipartite graph G is bipancyclic if G has a cycle of length l for every even 4 ≤l≤|V(G)|. For a bipancyclic graph G and any edge e, G is edge-bipancyclic if e lies on a cycle of any even length I of G. In this paper, we show that the bubble-sort graph Bn is bipancyclic for n≥ 4, and also show that it is edge-bipancyclic for n≥5. To obtain this results, we also prove that we can construct a hamiltonian cycle of Bn that contains given two nonadjacent edges. Assume that F is the subset of E(Bn). We prove that Bn -F is bipancyclic whenever n ≥4 and |F|≤ n-3. Since Bn is a (n-1)-regular graph, this result is optimal in the worst case.