Can we apply the Bellman-Ford algorithm to an Undirected Graph?

As a matter of fact any undirected graph is also a directed graph.

You just have to specify any edges {u, v} twice (u, v) and (v, u).

But don't forget, that this also means any edge with a negative weight will count as a loop. As the Bellman-Ford algorithm ONLY works on graphs that don't contain any cycles with negative weights this actually means your un-directed graph mustn't contain any edges with negative weight.