Bid'Daum's egg was found by the first Eragon during the most violent period of the war between the elves and dragons. Eragon raised the abandoned dragon hatchling as his own and when Bid'Daum grew strong enough to support Eragon's weight, the two traveled across Alagaësia, acting as intermediaries between the dragons and elves. The war ended as a result of their efforts, though both sides had heavy losses and would have destroyed each other if not for Eragon and Bid'Daum.
Later, the Order of the Dragon Riders was founded to ensure that peace and stability were maintained between all the races of Alagaësia. The order originally consisted of just Elves and dragons, but when humans migrated to Alagaësia, they were eventually accepted into the Riders' Order. The only races that were left out were the dwarves (because of their distrust towards outsiders) and the Urgals, but both were accepted later. The reason the Urgals didn't get the right to become Riders earlier, is apparent in their love for war and cruelty towards all races. If there were other reasons, they have never been approached.
Behind the scenes
Bid'Daum is often mistakenly identified as the white dragon who made a pact with the elves due to the fact that his scales are the same color. However, when answering readers' questions on the official Eragon site, Christopher Paolini answered this question.
- To clarify, Bid’Daum and the original Eragon convinced their respective races to make peace during the great dragon war. Then the acknowledged leaders of those races, Queen Tarmunora and the unnamed dragon, formalized the peace treaty. The fact that Bid’Daum was also white is merely coincidental.
It may also be possible that Bid'Daum may be the offspring of said nameless dragon (his name cannot be pronounced in any language), which would be logical in the sense that it would have been easier to convince the first among the dragons to endorse the peace and the joining if his kin were directly involved. However, this is nothing more than fan speculation. The fact that both are white doesn't really imply kinship, as it is reasonable to assume both that more white dragons existed and that scale color changed across generations as often as not.
The dragon's name is a possible reference to the Sci-fi epic saga, Dune, by Frank Herbert; the main character, Paul Atreides is known as Maud'Dib to the desert inhabitants of Arrakis, the Fremen. Bid'Daum is Muad'Dib backwards. Christopher has now confirmed the name relationship with Dune.