BACKSTORY
Thanks to the fact that Pokémon, being as expansive a universe as it is, doesn't spend too much time on its human characters, Bill's backstory is spotty at best and colored with a lot of hearsay. (Most of what you hear about him is from his fans, and it's not clear whether it's all second-hand or the result of a long chain of rumors.) Still, he's given a lot more history than a number of other characters, even if it tends to change depending on canon.
These are details that have been explicitly mentioned:
General/Multiple Canon
1. He was born and raised in Goldenrod City.
2. Sometime during his life, he moved from there to Cerulean Cape in Kanto, although he makes frequent returns to his hometown.
Games
1. [GSC/HGSS] His mother was (supposedly) a kimono girl. It should be noted that there are connotations associated with the kimono girl class as of Heart Gold/Soul Silver. As in, they're typically associated with the history or lore of the Johto region. Likewise, the Japanese word for the class is "maiko," implying that Bill's mother would have been in training to become a geisha when she met his father. What both mean for him is not specified (as is the truth of this tidbit).
2. [Crystal] His father was a Pokémaniac, and it's said that Bill took after him, implying that he's the reason why Bill became interested in Pokémon.
3. [Crystal] However, his father also has a tendency to hang around the Goldenrod Game Corner instead of work. It's not known how long this has been going on, but it's been stated it's been going on long enough to give Bill a headache about it.
4. [GSC/HGSS] He has two sisters, one of which is definitely younger than him.
5. [All] At some point, Bill had decided to be a trainer. The first Pokémon he caught (but not necessarily the first one he owned) was supposedly an Abra.
6. [GSC] However, he didn't enjoy battling. It's said he wasn't particularly excellent at it.
7. [All] At some point after his time as a trainer, he decided to switch focuses and go into scientific research. Specifically, his main interest was in Pokémon-related technology, with a particular focus on technology that served to connect trainers or otherwise make their lives significantly easier. With this interest in mind, he went on to develop an entire list of inventions that revolutionized the Pokémon world.
8. [RSE] Sometime after deciding to dedicate his life to technology research, he meets Lanette of the Hoenn region and, alongside her, co-develops the Storage and Retrieval System for the PC. While Lanette doesn't seem to gain much attention for it in her region, Bill becomes famous for it (among other things) in his. The Storage and Retrieval System then spreads to other parts of the world, including Sinnoh.
9. [All] Also during this time, he settled in Cerulean Cape in a house he calls the Sea Cottage. There, he conducts his experiments, including those involving the Teleporter.
10. [RGBY/FRLG] During one such experiment, he accidentally fused himself with a Pokémon (Clefairy in FRLG; unidentified in RGBY) shortly after meeting Professor Oak's grandson. Although he was able to develop a program to instruct the Teleporter to separate him from his Pokémon, he wasn't able to execute it by himself until he received help from a passing trainer, the hero avatar.
11. [All] Throughout his time as a technological expert, he has built a rather unique reputation. Thanks to his love for Pokémon (read: extensive collection), he has been given the nickname Pokémaniac by the residents of Cerulean City. Originally, this was meant to be an insult (as implied by an old man in Cerulean's Pokémon Center who goes on to say that the people who call him that are only jealous of him), but Bill decided to take it as a mark of honor, using it as a title in his introduction. Conversely, he has also garnered a lot of respect for fellow maniacs, including Celio, one of his research contacts, and Brent, a Pokémaniac in Johto. People have also been known to journey all the way out to Cerulean Cape specifically to see Bill's Pokémon collection.
12. [GSC/HGSS] Despite making his home in Kanto, Bill has, since moving, frequently returned to Johto to visit his family. In one particular case, he left his house in the care of his grandfather and spent the entire game (both Gen II and Gen IV) in Johto on an extended leave.
Electric Tale of Pikachu
1. Throughout his childhood, Bill hated school. It's not revealed why, but it is revealed that he wasn't a particularly excellent student in certain fields, ironically enough. By the time he left school, he wasn't able to spell "Pokémon."
2. The year he left for his journey was the first year children were allowed to take leaves of absences for Pokémon training. (In Electric Tale of Pikachu's universe, trainers who are still underage are still required to attend school. They can apply for leaves of absences that excuses them from attending, however, but these are only temporary.) Bill, who would do anything to get out of going to school, naturally took up that offer and left as quickly as he could.
3. Sometime during his journey, he obtained an Ivysaur. While Bill had previously begun to develop relationships with all of his Pokémon, it was the evolution of his Ivysaur into a Venusaur (a sight he describes as being awe-inspiring) that cemented his interest in the Pokémon world. He then decided not only to study Pokémon but also to make them the center of his entire universe.
4. Years later (presumably after going back to school and completing his education, given the laws of that canon), he got a job working with the Pokémon Cutting-Edge Technology Research Center... which is pretty much what it says on the tin. While working with them, he developed the Storage and Retrieval System, and he continues to maintain it while also working in their laboratories.
Pokémon Special
A lot of Special's canon when it comes to Bill is essentially identical to the games. Therefore, it's hard to go through all of the volumes and find something that isn't simply covered in on the roles page. Out of all of that material, these might be the most noteworthy additions:
1. He graduated from multiple educational institutions at a young age, implying that he most likely has a high-level degree. It's known thanks to Lt. Surge that he has at least gone through college.
2. However, considering that he is, in the Yellow arc, developing a thesis to present to Celadon University, it's implied that he hasn't finished attending school yet (or that part of his job as a scientist is to work for the university).
3. At some time in his life, he was hired by the Pokémon Council, an organization that oversees the activities of the Pokémon League (i.e., hires, pays, and/or dismisses gym leaders). He's climbed through the ranks of the council to become a respected member -- respected enough to serve as one of its advisers.