Rotten bananas are perfectly safe for cows to eat! In fact, in countries that produce bananas, cattle owners only feed rotten bananas to their cows. Their fresh bananas are eaten primarily by local people or exported to other countries.
Cows can eat the leaves from a banana plant, but only in moderation and only with other vegetables. The leaves often contain little nutrient value and the energy needed to digest them often outweighs their contribution.