Why does bilbo agree to join the dwarves in their adventure?

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!