Thinking about this, I don't think that he does. He was in The Defenders for quite a while, but are him and the Surfer close? Is he close with Strange? He can't be that close with Namor. I think it's the same with The Avengers. How close was he to Steve? Didn't Tony and him have a bad history? I really can't think of any other friends that Bruce has. Peter and the Torch have a long and close friendship, Peter and Daredevil are good friends. Does Bruce have anything like that?
I believe he does. Like Rick Jones, you had another sidekick Jim Wilson. Leornard Samson has been a dedicated friend and confidant of Bruce's over the year. Stephen Strange has been as well as being one of the few hero's to befriend both Bruce and the Hulk personas. The Hulk was always more comfortable as a Defender and though he and Namor clashed, underneath it was a mutual respect. The same applies for the Surfer. He probably had a closer relationship amongst the second tier of Defenders like Valkyrie, Hellcat, and Nighthawk than the Surfer or Namor.
Prior to the events of Civil War, it seemed as if Bruce had a friendly and collegial relationship with Reed Richards, and to a lesser degree with other Marvel geniuses like Tony Stark, Walter Lagnowski, and Hank Pym.