Why does Bilbo leave to join Bard and his men?

Bilbo leaves Thorin and co. to join Bard and the other people of Lake-town because Thorin forced him to do so. After the dragon Smaug destroyed part of their town, Bard and his people went to the Lonely Mountain to demand that Thorin and the Dwarves give them money, both for help they had given the Dwarves in the past and for damages done by Smaug. However, Thorin had already become entranced by the large...

Bilbo leaves Thorin and co. to join Bard and the other people of Lake-town because Thorin forced him to do so. After the dragon Smaug destroyed part of their town, Bard and his people went to the Lonely Mountain to demand that Thorin and the Dwarves give them money, both for help they had given the Dwarves in the past and for damages done by Smaug. However, Thorin had already become entranced by the large amount of gold in the mountain, so he steadfastly refused to give the Men anything, despite how warmly they were treated when they first arrived in the town after escaping Mirkwood. At the same time, Thranduil and the Elves demand that Thorin and the Dwarves give them money for services rendered in the past. Thorin refused them as well.

This infuriated both Men and Elves, and Bilbo realized that a war was about to ensue when Thorin called upon his cousin Dain for help. In order to avoid war, Bilbo used the One Ring to sneak out of the mountain with the Arkenstone, which was a family heirloom and what Thorin was seeking most of all. Bilbo gives the Arkenstone to Bard and Thranduil as a way for them to negotiate peace with the Dwarves, and then he returns to the mountain as if nothing had happened. When Bard and Thranduil arrive at the mountain with the Arkenstone, it comes out that Bilbo had given it to them, and Thorin is furious about this betrayal, so he casts Bilbo out of the mountain. Once he was out of the mountain, he decided to join Bard and his men in order to help in whatever way he could.