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.
I think it was Bilbo Baggins
Floating in barrels downriver.
as Bilbo was wanting to make peace so there is no war
The battle was just starting when the orcs showed up. They were the common foe of all and the elves, dwarves, and men fought against them instead of each other.
Bilbo found The One Ring (although he did not know it was so at the time, he only figured it was magical) and it became quite convenient to him. By slipping his Ring onto his finger, he was able to sneak away from Gollum, get out of the Goblin's caves, free the dwarves from vicious spiders who had caught them in their webs, and aid his dwarven friends in escaping from the wood-elves' castle.
the dwarves were captured by thorn and the wood elves long enough for bilbo to help them escape
They escape in barrels sent downriver to be filled.
I think it was Bilbo Baggins
He doesn't. Instead, he puts on his Ring and sneaks unseen with the captive dwarves in with them.
Yes, in chapter 9 the dwarves (but not Bilbo) were imprisoned by the Wood-elves in Mirkwood forest.
Floating in barrels downriver.
Bilbo stays invisible for weeks listening to conversations of the Wood-Elves. The king's first man<-? and a guard test some wine in the basement of the Wood-Elf compound. They fall asleep and Bilbo steals the guard's keys. Bilbo unlocks the cells of the dwarves and he puts them in empty tubs that the Wood-Elves were about to throw out through their river disposal system, (I can't quite remember what it was called), and the elves who throw out the tubs threw out the dwarves without even looking in them. Bilbo had one problem though, he wasn't in a tub, so he had to grab on to a barrel and float into the lake where the dwarves and Bilbo are accepted and fed and housed.
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.
After he breaks them out of the wood elves prison ....Thorin finally admits that Gandalf was correct, and tells Bilbo he IS what Gandalf said he would be.
as Bilbo was wanting to make peace so there is no war
He stole the guards keys, let all the dwarves out of their individual cells. Then he put them in barrels and let the elves throw them out of the "water gate" thinking the barrels were just empty and needed to be shipped to laketown.
In The Hobbit, they are simply identified as "Wood Elves". Later, they were further identified as being Silvan Elves led by the Sindar, Thranduil (who is the father of Legolas).