History:
Thousands of years ago, a young Rosalina, new in her job as Guardian Mother of the Galaxy, began to experiment with some of her new-found star power. She did not believe that any harm would come from using her star power on meteors to bring them to life, but instead in her inexperience she created a ravenous new species that sought only to consume. Horrified at what she had done, she sent the meteors away throughout the Galaxy. Eventually they wound up in Mushroom Space, where they would continue to devour everything, even Rainbow Road. 
After the disastrous introduction of Chain Chomps to the Grand Prix it was decided to use an Item that was similar, but far less risky for the activating driver. Bowser submitted his own Grand Stockpile of Bullet Bills, the Mushroom Kingdom equivalent to WMDs. Bullet Bills are created in Massive Factories in the Dark Land, and although sentient, are aware that they exist only for kamikaze missions. This combination of destructive power, spacial awareness, conscious decision-making, and unwavering loyalty makes them one of the most powerful forces in the entire Mushroom World. Being chosen to be an Item in the Grand Prix spares a Bullet Bill from its usually suicide mission, but such is actually against the Code of the Bills, which dictates that they die in battle. Thus, while being picked for life would seem like a huge relief, it is one of the deepest shames a Bill can suffer.
Chain Chomp appears in:
Double Dash!
The Chain Chomp only appears as a Special Item used by Baby Mario and Baby Luigi, as well as King Boo and Petey Piranha, who have access to all Special Items. It is dangerous and unwieldy and awesome and powerful at the same time. The Chomp will pull the racer at a rapid speed while knocking everyone else out of the way. The Driver himself though, is not invulnerable, and still susceptible to dangers on the course. It is also uncontrollable, the Chomp will tug the racer straight into danger, or suddenly leave before a cliff or turn that may pull the racer into oblivion. Still, the Chomp takes up nearly the entire track, and avoiding one coming up from behind is very difficult.
Bullet Bill appears in:
DS
Wii
7
The Bullet Bill in later games is very much a refined version of the Chain Chomp. It pulls the player ahead and destroys all other obstacles in its path. The key difference is that it encapsulates the racer, rendering him or her invulnerable to any disaster on the track. The Bullet Bill can supersede any danger besides a Star. It conquers Mega Mushrooms, and is unaffected by Thunder, POW Blocks, or Bloopers. There is still some danger of it wearing off and leaving racers flying headfirst over a cliff, but the benefits far outweight this mild risk. It's arguably better than a Star, especially on difficult tracks where it will take over the driving and launch the racer ahead. There isn't the danger of screwing up or junking turns because of high speed handling. Bullet Bills are game over, man - they only appear for players who have fallen far behind, but they offer a great advantage.