How do Bilbo, Thorin, Bard, and Gandalf embody the qualities of a hero and how do they not??

They were heroes in that they went above and beyond the call of duty to do something that many others would not have attempted. I think that is what a hero is. It is not someone who sets out to save the world, but someone who ends up doing it quite by accident. Bilbo could have stayed home, safe in his Hobbit hole and never had an adventure at all. Bard could have chosen to run away or hide and let the people of the town fend for themselves; instead he chose to try to kill Smaug. Gandalf chose to involve himself in the affairs of Men and Hobbits and Dwarves when he could very well have not. So it was the choices they made that made them heroes......they did not take the easy or safe way, but the way that seemed right to them.