Bubble Bobble Part 2 is a game in the Bubble Bobble series. Never released in the arcade, two versions of the game were developed independently from each other (for the NES and Game Boy formats), with each game receiving a different storyline as a result. The Game Boy version is known in Japan as Bubble Bobble Junior.
(This entry is for the NES title)
According to the NES version's manual, this game would supposedly star Bub and Bob as the original duo. However, the protagonists are actually intended to be Cubby and Robby, their descendants (hence the name "Junior" used both in the NES game's bonus rounds and in the alternate title of the GB version).
As seen in the game intro, Cub, and a girl named Judy, were sitting in a park. Suddenly, a floating skull character captures Judy into a bubble, and sends her and Cub into the air. Two characters named Drunk (from the original Bubble Bobble) follow the skull and take Judy away. Cub turns (or is turned) into a bubble dragon and heads off to rescue his girlfriend. There is also a two-player mode, implying that Rob has suffered the same events as Cub had. However, the manual states that Judy is a friend of both.
Because of its late release on the NES, Bubble Bobble Part 2 is exceptionally hard to find and is sought after by collectors.
Source: Wikipedia, "Bubble Bobble Part 2", available under the CC-BY-SA License.