The answer is YES. A bipartite graph with no edges is known as the trivial bipartite graph.
P.S. I asked this same question, into my classroom into IIT. I asked him that, is it possible that vertex set and edge set can be empty?
First, he laughs, then he said, We can not make vertex set empty otherwise, there will not be any graph, and yes we can make edge set empty and that will be called trivial bipartite graph.