In chapter 1-3
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His Took side of the family urges him to take a chance.
At first he's almost relieved that the dwarves have left ahead of him, and he feels he's out of it...... no adventure for Bilbo. Fortunately, Gandalph brings Bilbo a note from Thorin. It's a thank you note, which cites his "grateful acceptance" for his (Bilbo's) offer of "professional assistance." And then off he goes!