1980-1981:
In the episode "Zatanna", a conversation between Bruce & Alfred insinuates that the last time they saw Zatanna and her father Zatara was 12 years ago. The episode is set in 1992, so 12 years before that brings us to 1980 as the date that Bruce ended his training with Zatara and headed to Japan.
In the episode "Night of the Ninja" there are more flashbacks set in Japan, which continue this narrative, featuring Bruce training with Kyodai Ken under Yoru Sensei. We know that Bruce is back in Gotham in 1982 because that's when the flashbacks from "Batman: Mask of the Phantasm" take place; less than 11 years before that feature film. So that's how I figured Bruce spent 1980-1981 training with Yoru Sensei.
It seems unlikely that Bruce could master all his martial arts skills from just 2 years with Yoru Sensei, so I theorize that Bruce had earlier trained with the senior monk in Nanda Parbat known only as The Master, as revealed in the JLU episode "Dead Reckoning":
"He knew The Master even before I did." - Deadman
"He was one of my martial arts teachers." - Batman
So it would seem the 2 years spent with Yoru Sensei were spent learning new styles of combat to compliment his previously learned skills.