It’s unclear why the Bai people of Yunnan call themselves “Bai.” The history of the various ethnic groups in Southwest China is quite obscure, and there’s a degree of arbitrariness to the official categories, which date from the 1950s.
There are other groups which are sub-divided by color on the basis of their dress, like the Miao – there are White, Blue, Flower Miao etc. But that’s not what’s going on here.
One fact that’s possibly relevant is that with one of the other prominent ethnic groups in Yunnan and Sichuan, the Yi, society was based on a caste system where the dominant, aristocratic group was “Black”, and the subservient commoners were “White.” According to a 1997 paper by Pan Jiao in the journal Inner Asia, this distinction wasn't based on skin color, but the Yi believed that the aristocrats had “hard bones” and others (there were also slave groups) did not. White Yi had to pay tribute to their Black masters and perform labor duties and military service. Black and White Yi didn’t intermarry, and the system was only brought to an end in the 1950s under the Communists. Regarding the Bai (who of course are not now considered part of the Yi ethnicity,) there are other Yi subgroups living in proximity to them, like the Nosu or Nasu, whose name means “black.”
Also, some Chinese historians of the region point to a distinction in the historical records between the 白蠻 and 烏蠻 (white and black southern barbarians.) The Baiman seem to have lived in the Western Cuan area between Kunming and Dali, and the Wuman in the Eastern Cuan area (eastern parts of Yunnan.) The Baiman generally had more advanced agricultural techniques than the Wuman, which would line them up with the current Bai minzu. For more on this, see Steven Harrell, “The History of the History of the Yi,” the section called “Ma Changshou’s account of Yi history,” p. 84 and after, esp. p. 87 (link below.)
It's probably wise to treat the name of this ethnic group as simply a name, and not make any claims regarding its etymology.
The History of the History of the Yi