I have taken a small example here.
Lets consider K4,3
The attached diagram shows the graph and the BFS tree.
Height = 2
Explanation: In a bipartite graph, the vertex set can be partitioned into two disjoint sets. Lets consider the two partitions as U and V. Lets take a vertex from partition U as source. Then the BFS tree will contain all the nodes of partition V in height 1, since the source is connected to all the vertices of V. Now, we take a vertex from V which appears in the BFS queue after the source. Since it is connected to all the vertices of U, we include all the vertices of U in height 2.