Depending on who you talk to, and what medium it is, there's always someone different who trains Batman. Most famously, Bruce Wayne traveled around the world, learning from various masters of both martial arts, scientific prowess, and other fields he felt would be good for his training.
One name though does occur a few times, Henry Ducard. In fact, in the Dark Knight trilogy, he was the sole man who trained Bruce Wayne in the ways that would lead him to be Batman.
Both in the movies and in the comcis, Ducard thought of Wayne like a son of sorts, and taught him all he knew. Which for the record, was not insignificant. But both times, Bruce's morality would conflict with Ducard's, and would both times lead to his eventual death.