Bruce Banner had stayed at Stark Towers for 3 months after the incident in New York, helping with clean up and consulting with SHEILD, before he felt the need to leave. Its not that he wanted to leave, he liked living with Tony and the rest of the misfit team that he called the Avengers, it's that he needed to leave.
He had been doing good in New York, he was helping. But, as Bruce learned many times in his life, good things don't last. He had to leave before he messed up and hurt someone or destroyed something.
That's why he donated the majority of the money he made from the consulting work he did with SHEILD (he wasn't doing that work for free) back to SHEILD and to New York City to assist with repair of the Helicarrier and the parts of the city the Hulk had help destroying. He took the rest of the money and bought a plane ticket to Calcutta and left.
He didn't tell anyone he was leaving, he didn't say good-bye, he didn't leave a note saying where he was going and why. He needed to disappear and he didn't need Tony or the rest of the team to convince him to stay. Because if he stayed longer, he was bound to smash something.
He arrived in Calcutta and continued where he left off before Natasha got to him. Well, he was a little better off now that he had a little money. He was able to afford a small apartment instead of bartering for a place to stay and food. Sure it was just a bedroom with a bathroom and a small kitchen attached to it, but it was more than he had before and he was grateful.
He got back into the same familiar routine that he left. He worked to help the sick and the poor and make the world a little bit of a better place. He tried to forget the team he left and he hoped they, and the rest of the world, forgot about him, they would be better off.