How did The Hulk end up in India?

In a way it did. The ending of The Incredible Hulk we see Bruce attempting to control the transformation, a few years later in The Avengers we see that he has succeeded in gaining some control over the Hulk. We can then assume that his trip to India was probably part of that training process. When Bruce meets Natasha for the first time this conversation between them occurs which may shed light on the subject:

Bruce Banner: Should have got paid up front, Banner.

Natasha Romanoff: [comes up behind him] You know, for a man who's supposed to be avoiding stress, you picked a hell of a place to settle.

Bruce Banner: Avoiding stress isn't the secret.

Natasha Romanoff: Then, what is it? Yoga?

And a bit later in the same conversation:

Bruce Banner: And what if the... other guy says no?

Natasha Romanoff: You've been more than a year without an incident. I don't think you wanna break that streak.

Bruce Banner: I don't get always what I want.

A large part of Bruce Banner's self control is based on distracting himself and thus mentally distancing himself from being The Hulk.

Now how does he do that?

Banner being a world class physicist employs his immense knowledge ( He is described by Marvel comics as "possessing a mind so brilliant it cannot be measured on any known intelligence test."1) in humanitarian efforts. He thus lands up in Calcutta(India) where he is just another foreigner, far far away from the United States and is practically unrecognizable.

Here he immerses himself in fighting the endemic spread across the city and his work becomes his savior. It is safe to assume that Bruce Banner keeps traveling (and quite frequently) to far-flung places where he can be a contributing member of the society through his work and keep himself distracted enough to not turn into that "Green-Rage-Monster".

In the end of The Incredible Hulk we see Banner meditating and gaining some control over his transformation. Whether it is true or not but the stereotype is that India is a good place if one wants to engage in spiritual studies, meditation or yoga type activities. (It's true. I know ;) ) Plus, Banner being a brilliant doctor and a good person at heart (when he's not busy being a rage monster) might have been attracted there by reading about the endemic prevalent in Calcutta and traveled there with an intent to help the sick and poor.