National Geographic offers excellent advice on photographing an elephant in this article.
But here's another suggestion: Arrange to travel with CLIC Abroad and international photographer D.K. Bhaskar. Not only will you see large numbers of elephants in southern India, but you will also be spending time with a man who devoted his life to photographing large mammals.
This is photo of tribal mahouts bathing an elephant at the Anechowkur Elephant Camp on the Nagarahole National Park. CLIC Abroad and Bhaskar have led several trips to Anechowkur and Nagarahole, and they formed the foundation for the documentary "Elephants in the Coffee."
Because of Bhaskar's extraordinary contacts in the region, photographers traveling with CLIC Abroad have been able to get close to elephants, and obtain dramatic shots. And when you're as close as Bhaskar takes you, you don't need to worry about a long lens.