At the end of the story.
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Bilbo had lost his reputation in Hobbiton because he was now an adventurer. Other Hobbits found him odd and his adventures were considered not "Hobbit-like." Hobbits felt he was no longer the Hobbit that was contented to live in the quiet Shire
Asian's answer is excellent. Hobbits loved nothing more than caring for their homes, sharing a large meal, and socializing with family and friends. No one left the Shire, no one even thought about it. For Bilbo to leave, especially for reasons that would be seen "wordly" by his neighbors would have been disapproved of. Thus, his reputation slipped a bit.