One of the most interesting things about Bulma has been her constantly-changing hair. Throughout Dragon Ball and Dragon Ball Z, she had a general tendency to change her hairstyle; she could have anything from a bob cut to a ponytail to an afro. She's been through more hairstyle changes than any Super Saiyan could hope to match. However, something that's not as talked about is how often the color of her hair changes.
Just as Bulma's hair color has changed throughout the franchise, so has her natural hair color. It's not as frequent, but she's gone from turquoise to purple to blue hair, and fans have just been expected to accept it without question. These hair changes have also influenced her children, Trunks and Bulla; their hair colors are constantly changing, and it has less to do with being Saiyans than one might think. For a better idea of how the Brief family's hair has changed over time, here's a look at the changes and why they may have happened.
Bulma had the classic turquoise-colored hair for the first two chapters of the Dragon Ball manga. This is likely why Toei Animation initially chose to give her turquoise hair for the anime and kept it in the years to come. Thus, turquoise is the hair color she's best known for having.
However, Bulma was depicted as having purple hair rather than turquoise for the rest of the Dragon Ball manga. The reason for the color change is unknown, but purple was the color Akira Toriyama committed to. He even depicted Trunks and Bulla as having inherited purple hair from their mother. At least in the manga, purple hair is a dominant gene in Bulma's family.
For how Bulma's children are depicted in the manga, it's strange to think of how they turned out in the anime. For example, Trunks, despite being confirmed as Bulma and Vegeta's son, was given the same purple hair he had in the manga. If the anime wanted to be consistent, then perhaps they should have given Trunks the same turquoise-colored hair they gave his mom. It's possible that Trunks was allowed to keep his purple hair because, unlike Bulma, he never had turquoise hair in the manga.
Bulla's hair change is a little harder to pin down. Like Trunks, she was never shown with turquoise hair in the manga, yet it was given to her for the anime. It's possible that she was given this special treatment because she was the spitting image of her mother. Giving her turquoise-colored hair was the ideal way to complete the look.
Bulma and her children maintained their anime hair colors throughout Dragon Ball GT. That said, Trunks' hair was made a darker shade of purple. This isn't necessarily a color change, but the dramatic change in hue is definitely noteworthy.
Bulma actually was given her purple hair for the 1996 Dragon Ball movie, The Path to Power. This movie was written as an alternate telling of the original Dragon Ball; it combines and reworks story elements from the Son Goku Saga and the Red Ribbon Army Saga to create a new tale altogether. Since this was a reboot and it wouldn't really tie into anything canon, any creative liberties taken with the story were fair game, including Bulma's hair color.
For about another two decades, Bulma's official anime hair color remained some shade of turquoise in most media. It was like this in video games and promotional material, but also OVAs like Yo! Son Goku and His Friends Return!! and Plan to Eradicate the Super Saiyans. She even kept her hair turquoise throughout the Battle of Gods movie. That latter example is odd considering what comes next.
In the sequel to Battle of Gods, Resurrection F, Bulma's hair color changed from turquoise to a darkish blue. It's unclear why this change was made, as there is no direct mention of it in the story. Judging by the character's lack of reaction, Bulma is meant to be seen as having always had this dark blue hair.
Toei Animation would roll with the decision to make Bulma's hair dark blue going into Dragon Ball Super. When adapting the Battle of Gods movie into an arc, Bulma was given a sort of in-between shade of turquoise and blue hair; this may have been done to make the transition slightly jarring. From the Golden Frieza Saga onwards, Bulma would continue to be depicted with dark blue hair.
This color change affected her children, starting with Trunks, confusing the issue even further. The Trunks from the future was given dark blue hair just like his mother's. However, the young Trunks in the present still has his purple hair left over from his DBZ days.
One could argue that modern Trunks' hair was kept purple to distinguish him from Future Trunks. However, that same modern Trunks was also given blue hair in Dragon Ball Super: Super Hero. All of this is to say nothing of the introduction of Super Saiyan Blue, a transformation that's apparently inaccessible to any version of Trunks. As with Bulma, Future Trunks' hair turning blue might be something fans are expected to accept as though it was always like this.
The same thing happened to Bulla's hair color. She may have had turquoise hair in the DBZ anime and any other media preceding DBS, but once that threshold was crossed, her hair was made blue just like her mother's. It's worth noting that when she was born, she had that same transitional blue Bulma had at the start of DBS. It's also worth noting that the two got lighter shades of blue hair starting in Dragon Ball Super: Broly; of course, most of the characters' color palettes were altered slightly starting with that movie.
It is especially perplexing how Bulma and Trunks appear as though their hair was always dark blue, not just in DBS. In the "Boogie Back" ending, Bulma's Chapter 1 self was shown with hair just like her early DBS self. Trunks was shown in a flashback to his time in the Hyperbolic Time Chamber; the colors were removed from the scene, but that might have been done to avoid controversy. Changing the Brief family's hair is nothing new, but this borders on revisionist history.
Finally, for the sake of completion, there are some miscellaneous hair-color changes worth noting. Trunks can change his hair to golden yellow when he becomes a Super Saiyan; Bulla might be able to do this, too, if she ever trained to be a fighter. Xeno Trunks of Dragon Ball Xenoverse and Dragon Ball Heroes fame maintains his iconic purple hair despite residing in the Time Nest in the distant future; he can also become a Super Saiyan God, which turns his hair bright red. Bulma in Dragon Ball Evolution doesn't have naturally-blue hair since that's impossible in real life, but she has a blue dye streak to nod to her anime counterpart. The Future Bulma in DBS had her hair changed from turquoise to the same dark blue as her present counterpart. Most of these changes aren't too big of a deal, but they're worth considering.
The Brief family's hair could technically be called blue throughout the Dragon Ball franchise. Whenever anyone refers to Bulma's hair color, it's referred to as blue, whether it's blue or some shade of turquoise. Besides that, turquoise and purple are just shades of blue with other colors mixed in; they could arguably be called bluer than that other color. In this sense, saying that Bulma, Trunks, or Bulla are blue-haired wouldn't necessarily be wrong, just misleading.