I feel as Bruce is altruistic enough to not be overly concerned about his own life, even if he knew of something that can end the Hulk. He even tried to kill himself. Sure, depression may have lead to that as much as anything else, but I feel as though one of his biggest fears, aside from hurting the innocent/those close to him, is being captured by General Ross and having the power of the Hulk drawn out of him and abused.
So in addition to everything else that may have lead him to put a barrel in his mouth in the middle of nowhere, I think denying Ross of his prize may have been a motive.
Of course now that Bruce has something to live for (assuming the events of AoU don't completely destroy his faith in teamwork and his role in the world, essentially putting him back in a mindset similar to pre-Avengers), you could argue that threat of death may be an issue for him again, but I think it may require a near-death experience first. As you said, he doesn't really feel fear.
He seemed pretty cocky about not being able to die in his Avengers dialogue. I guess surviving a bullet to the brain will do that to you. So maybe that went to his head (har har), and you have to deconstruct that before you can explore fear of death as a theme. So what earthly thing could almost kill the Hulk, but not quite do the job enough so that Bruce can be shaken up about it afterwards?