Don’t expect Bulls coach Tom Thibodeau to go to New York. Not this summer or any time soon. He won’t be sniffing around his old stomping grounds in Minneapolis this offseason, and he’s not Hollywood enough for Los Angeles. He’s a Bull — and not just because he has a contract for three more seasons or because this was the team that gave him his first chance to be a head coach. It’s because Thibodeau also picked the Bulls. ‘‘When I was an assistant, I was fortunate to be involved with some really good teams,’’ Thibodeau said. ‘‘That’s why I wasn’t anxious to take a bad job.’’ Like most everything in Thibodeau’s life, his decision to take the Bulls’ job before the 2010-11 season was well-thought-out. It was about which franchise could he grab hold of, implement his culture and still have the backing of a front office that was focused on winning. ‘‘Your best players have to sell what you’re trying to do with the team,’’ Thibodeau said. They have. They’re all in. That’s why even with the Bulls down 0-2 in their first-round playoff series against the Washington Wizards, none of the players seems intimidated. It’s not in their makeup to flinch. Thibodeau won’t have it. Not that establishing a culture like that came easily. It was a process early on — and one that had to be implemented with as little resistance as possible.