The first thing that changes about Bilbo Baggins during the course of his quest is his physical nature. He becomes stronger and hardier and thinner.
Another thing that changes is due to the effect of his discovering the one ring. He becomes somewhat deceitful and sneaky. He lies to Gandalf and takes on some of the character of Gollum.
Another thing that changes is his ability as a thief and his willingness to steal. At the beginning of the novel, the dwarves and Bilbo are equally unsure of his thriving abilities. By the end, he has become a successful thief (although somewhat by accident).