How to find the shortest even length cycle in a bipartite graph?

If you have n vertices and m edges, how would you find the shortest cycle of a bipartite graph in O(n^2) time? To do it in O(nm) time, it is simply a BFS on every single vertex. I do not understand how you can do it just by going over every single vertex. I know you would have to stop at non-tree edges to do so, but how would you use this type of technique to guarantee this runtime and find the shortest cycle? Could anyone give me some sort of advice or help?