Bulma is a highly intelligent woman first seen as a 16 year old girl searching for the legendary Dragon Balls so that she can use them to make a wish for the perfect boyfriend, or something like that atleast. Using the Dragon Radar she invented, she eventually bumps into a young boy named Son Goku, who has his grandfather's four-star Dragon Ball. The entire Dragon Ball series kicks off from here with Bulma and Goku searching for the remaining Dragon Balls together.
Bulma is the daughter of Dr. Briefs, the founder of Capsule Corporation which specialises in making small capsules that can contain virtually anything of any size within them, and yet be small and light enough to carry around in your pocket. As with her surname "Briefs", her first name is also a play on an undergarment, in this case a play on the word "bloomers". Her original Japanese name "Buruma" is the name of a brand of popular gym shorts worn by girls in Japan. This underwear naming-scheme carries on in her family with her son being named " Trunks" and her daughter " Bra". However her daughter was named "Bulla" rather than Bra in the Funimation dub, which upset some fans of the series.
Bulma puts her technical skills and amazing brain to good use throughout the Dragon Ball/Z/GT series. Although she is mostly known as being the inventer of the ever-useful Dragon Radar, she also modified Raditz' scouter to display their own language so they could read it. She also made copies of Vegeta's Saiyan Armor for Goku and the others to wear during their training in the Hyperbolic Time Chamber. The Bulma from the alternate timeline that the original Trunks belongs to also invented the time machine he used and in Dragon Ball GT, Bulma built a Blutz Wave generator to allow Vegeta to transform into an Oozaru without his tail.
Bulma is a parody of the character Xuanzang from the Chinese novel Journey to the West.
Bulma has a romantic relationship with Yamcha during most of Dragon Ball and at the beginning of Dragon Ball Z. She eventually ends their relationship and forms a life-long relationship with Vegeta. They presumably get married at some point, have two children together named Trunks and Bra and live together at the Capsule Corporation. Even though Vegeta can be very arrogant and rude to her at times, he doesn't scare her one bit. She sometimes argues with Chi Chi about whos husband is better looking.
In the Dragon Ball manga, Bulma's hair is purple while in the anime and most video games, her hair is turquoise (somewhere between blue and green). Her skin is a pale milky colour and her eyes are blue. Her outfit and hairstyle constantly changed throughout the anime. She has a slim figure and sometimes uses her good looks to get what she wants. She is often harassed by Master Roshi who is usually trying to grab her breasts, which were apparently revealed to be a 34C. She has had many topless and even a few nude moments in the Dragon Ball anime, which were either censored or in a few cases removed completely from the Funimation, Ocean and other dubs. Possibly the outfit worn the longest without change by Bulma was the outfit she wore while on Planet Namek. Apparently Bulma has had somewhere close to 20 different hair styles throughout the anime, and even more outfits than hairstyles.
In Video Games
Bulma usually makes very minor appearances in video games, either helping the player, selling them items or simply appearing briefly in cutscenes. However there was, buried deep within Dragon Ball Z: Budokai 3, a full 3D model of Bulma just like the 3D models of the playable fighters. Also in the DVD packaged with the special edition of the game, her voice actor is seen recording fighting sounds. She could in fact be unlocked using a cheat disc, however she is nothing more than a template with no moves or skills. Bulma is playable to an extent, by using the cheat disc to set her character model as an alternative costume for Videl.