Didn't Bruce have part of his training take place in Europe ? With thieves or pickpockets or something like that ? I think I remember that from the comics but I might be wrong.
That was from the leaked Batman Begins script, but the scene never made it into the filim. Wayne definitely trained elsewhere before meeting up w/ Ducard though, as he's already a formidable martial artist by the start of the movie. Ducard initially beats Bruce down only because he's in a clearly weakened state, then assists in honing his skills and teaching him further.
As far as the comics go...
Author Alan Grant writes,
"At age 14 he [Bruce] traveled to Europe, studying at Cambridge University, the Sorbonne in Paris, Berlin School of Science and a dozen other places, never staying for long. He spent his evenings with the denizens of the street, learning less savory skills. At age 20 he entered the FBI and stayed for six weeks before realizing that shuffling papers was no way to fight crime."
"The grim purpose that burned inside him was growing, demanding direction, seeking release. He looked further, to the East. He learned karate from an ascended master in the Paektu-San mountains of Korea--Savate from a convicted killer living as a beach bum on an island off Borneo. Six months in a Japanese hermitage taught him the value of Judo and Ju-jitsu.
From a Chinese woman so old she should have been dead, he learned the secrets of the Tao, that nothing is fixed, everything is fluid, everything is energy. He mastered a dozen disciplines, experimented with them and fused them into something that was uniquely his own. In Africa he learned how to read the environment for the signs man's passage leaves--how to find and follow a trail to which ordinary men were blind...
The ninjas taught him their secrets--how to use the shadows, how to employ psychology to win the battle before it's even fought--the precautions to take when you make yourself a target--and how to use fear."
