He was gone for seven years, so I had always assumed it was about two or three years of travelling and four or five years of training.

i am assuming that the training he got from before the league of shadows encounter, happened at intervals during his travels

I always thought he was abroad for five years (Give or take) and spent a few months in that prison.

Then he trained with the League of Shadows for almost a year.

To me the league training seemed to take less than a year. Bruce climbed the mountain in the fall, trained during the winter, and then he left sometime in the spring or summer.

But it is hard to know for sure in that mountain climate and your guess is as good as mine.

It didn't state it outright in the novalization, but it did hint that Bruce spent at least five seasons (two winters) with the League of Shadows. So I think it would be something like five years of travelling, a few months in prison, another few months in another prison, and over a year of training.

And yes, Bruce landed himself in two different prisons on two different occasions.
When he was caught giving a hand smuggling (his own) merchandise in the movie, he got send to his first prison. On the immediate next scene, he was actually going to his second prison.
Bruce got out of his first prison because he had some connections with the Chinese blackmarket (I think), but it ended up being a setup of some kind because the Chinese mob needed a few scapegoats for another mission. So Bruce ended up in another prison a few weeks after he got out of the first one (and stayed there...until Ra's).