He doesn't. Instead, he puts on his Ring and sneaks unseen with the captive dwarves in with them.
the dwarves were captured by thorn and the wood elves long enough for bilbo to help them escape
Bilbo kept from being captured by the Wood Elves in Mirkwood by using The Ring to turn himself invisible. He slipped in after the company of Elves that had captured the other members of The Company (namely, the twelve dwarves) as the Elves were escorting the dwarves into the Elven fortress.
as Bilbo was wanting to make peace so there is no war
They escape in barrels sent downriver to be filled.
Bilbo gets lost in the tunnel with Gollum, The dwarfs nearly get eaten by spiders and then they get captured by elves, and Bilbo nearly causes a war by giving the elves the dwarfs most prized possession.
I think it was Bilbo Baggins
They took them to the halls of the Elven King in his hall, a large cave at the edge of Mirkwood. The wood elves of Mirkwood, in the Hobbit, took the thirteen dwarves to their king's halls, where they were locked in by cellars and a magic gate.
The Dwarves will get captured by the giant spiders who plan to eat them, Bilbo rescues them, only for them to be captured again by the Elves.
The dwarves were captured and imprisoned by the elves in Mirkwood. Bilbo had to keep entering to form a plan and carry it out.
The elves.
Floating in barrels downriver.
{| |- | In Chapter 9 of The Hobbit, the dwarves were captured by the elves. They had just escaped from the spiders in the previous chapter and were wandering around the forest. They were hungry and looking for food when they encountered the elves' feasting in the woods. After several failed attempts to 'crash the party' they were all captured, except Bilbo, who used his ring to escape. |}