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?
During World War Hulk, Hulk referred to the Surfer as the only one of his fellow Defenders who was worth a damn. The Surfer offered to take Hulk back to Earth in Planet Hulk, but the Hulk declined and the two parted as friends.