I mean in the comics not the Nolan films.
15 years I think. There's a cool story in Legends of the Dark Knight called "I hate when he does that" about a young Bruce in training, the story takes place in Thailand, and at the end of it he's planning on going to Eygpt. I'd love to read more stories about this part of Bruce's life and started a thread about it:
Due to the sliding time scale and variable ages, there's few exact numbers as to how long. What IS known is that he trained all over the world, in pretty much every style of martial arts known to man. He also learned various other things he'd need, such as detective skills, stunt driving, skills in sneaking, etc.
It was once said that he trained over-seas(not specific as to where), but assumed somewhere in Southeast Asia among other places. He spent 12 years on his journey and trained in Chemistry/General Sciences, Varied forms of Martial Arts, Burglary(Ninja Style), and Manhunting.
Didn't his parents die when he was around 6-8 or maybe 10 years old? In that case he would have commenced his education shortly after, and his physical training not long after that. In Batman: Year One, it is said he had waited 18 years before he finds his purpose and identity as Batman. In that case, indeed it took 18 years to be Batman if you count his education as well as physical training. He is believed to have travelled around the world, in places such as Asia, learning all he needed to know: Martial Arts, Criminology, Chemistry/Forensics. Pictured is the Year One image as well as his origin story.
As stated before, he's trained all over the world. Japan, France, etc. Brazil too I believe. He's a master of Jiu Jitsu, as well as many other forms of martial arts. I believe he trained as a Samurai or Ninja in Japan as well. France he was trained as an assassin by Henri Ducard. David Caine also was one of his many mentors, who was a member of the League of Assassins.
As for how long, the simple answer is a little over a decade. You could argue though that he is still learning and training today. Every villain he fights, and mistake he makes improves him as Batman both physically and mentally.