Bulma is the daughter of Dr. Briefs; the founder of the Capsule Corporation. She is a beautiful woman with purple hair in the manga and blue/green hair in the anime. As with her entire family, her name is a play on a type of underwear, in her case bloomers. Her last name is also another type of underwear, briefs. As she is the daughter of the founder of Capsule Corp., she is very wealthy.
Major Story Arcs
Bulma meets Goku at a young age. She was searching for the seven Dragon Balls. When she found Goku, she noticed that Goku had the four star Dragon Ball. Not willing to give it up, Bulma lets Goku joins her and they go off traveling the world searching for the remaining Dragon Balls. On their adventures they find people like Yamcha, Oolong, Master Roshi and others. After many adventures, Bulma eventually stopped seeing Goku. After many years, she sees him again at the 23rd Tenkaichi Budokai (World Martial Arts Tournament).
Dragon Ball Z
When the Z-fighters needed to go to planet Namek, Bulma and Mr. Popo located a space ship used by Kami to arrive on Earth. She fixed it up and she went to Namek with the Krillin and Gohan. During her time there, she miraculously survived the perils of the planet by herself. When her luck finally ran out, she was saved by Gohan.
Bulma would try her relationship with Yamcha again, but to no avail. During this time, she had a relationship with Vegeta and gave birth to their son Trunks. While never seemingly close, they had great love for one another.
During the days when Buu was trying to destroy the world, she stood lookout on Kami's lookout for Buu. She eventually was killed by Buu. Later, she was resurrected by the Dragon Balls. Her and Vegeta would have a daughter named Bra.
Powers & Abilities
Bulma is an incredibly brilliant mechanical genius just like her father. Bulma's most famous invention is the Dragon Radar used to locate the magical Dragon Balls. In the bleak timeline of future Trunks, she designed and built an operating time machine.
Bulma also seems to have uncanny good luck.
She doesn't have any superhero powers or abilities but she does know how to operate guns and some weapons. She is no stranger when it comes to using gadgets. In the Dragonball, Dragonball Z, and in the Dragonball movies she is a very respected mechanical and electrical engineer like her father.
She can repair spaceships, cruisers, and all types of computerized and electrical based gadgets. She is also a very experienced pilot.
Alternate Future Timeline
In an alternate future, Goku dies of a heart disease and the evil Androids 17 & 18 wreak havoc on the Earth, killing all of the Z-Fighters except Trunks. Bulma is able to build a time machine to send Trunks back in time.
He is able to not only change the past but train with his father to ascend new levels of power. When he returns to his own time, he is able to destroy the androids as well as Cell and start a new future with his mother.