Yes, Bilbo did not expect to be a hero. However, he did have what it takes to be a hero. He turned out to be brave, and intelligent. His services were vital to the mission's success. The biggest mistake he made was taking the ring and keeping it secret.
Bilbo is an unlikely hero in this story. We are told that Hobbits are quiet, reserved people who don't go away from home. Bilbo sets out with a group of dwarfs because they need his help. He is repeatedly draw into conflicts along side this group and shows himself to be quite capable despite the fact that he has never been away from home before. As the story progresses, we see Bilbo move from the accidental hero to something far more intentional. Many times he could have run away and saved himself at the expense of his companions, but he does not. Bilbo does what he believes is right whether others agree with him or not. In the end, it is because of Bilbo that the missions succeeds. Bilbo becomes the hero even though he is the one least likely to hold such a position at the start of their journey.