BB is the underclassman (kouhai-kei) devil heroine that dashingly appears on the far side of the Moon.
She usually hides her devil tail, and holds a teacher’s pointer in one hand. Always behaving with abandon, she thinks she is a god, and is always making illicit modifications to SE.RA.PH.
She is an out-of-control AI that brought about the events of CCC.
She was formerly a management AI of the same type as Sakura, but due to a bug her self-preservation system went wild, and for some reason she came to the conclusion that, “No matter the sacrifice, I must continue to exist.” and turned into a continuously growing monster that absorbs NPCs, Servants and Masters.
She openly hates humans, and makes the protagonist and company suffer by dropping them on the far side of the Moon.
She refers to herself using “watashi” [わたし].
She calls the protagonist “senpai.” She addresses humans by their family name and adds “-san” but she addresses Servants with only their name.
BB assumes that she is normal, but if you look at things objectively she is clearly crazy. Her frequently yandere-like actions come to mind, but rather than explaining here, please refer to the game itself to find out the reasons behind them.

BB is the true heroine of CCC.
In the first half of the game she is treated as a criminal who takes delight in people’s reactions to her crimes.
In the second half of the game she is treated as an enemy of humanity that must be defeated.
Her actions thoroughly reflect her “human-hating, innocently-cruel Queen” character, but the road that led her to be like that was brought about by a single trivial mistake.
For some reason she decided to fight against Moon Cell (the world), despite the fact that Moon Cell’s destruction would also mean her own destruction. Upon realizing this contradiction she caused herself to go crazy (go out of control). When she realized the truth of the situation, she asked herself the following.

“It’s not logical. There’s just no reason, no value for me to do such a thing.”

This problem poses a question that the player must also address during their play through.
If you were to use Fate/stay night as an example, Emiya Shiro’s actions (heroic nature) are appropriate for the affection he holds for Saber or Rin, but in CCC there is no chance for the protagonist to demonstrate their heroic nature.
However, the AI who was once just a puppet closed her eyes for the last time with a satisfied expression on her face.

“More than special words and a helping hand offered by some human special to me, the words that came from you, someone who can be found anywhere, who was always there doing your best to make me laugh, made me happy.”

Certainly any girl dreams of being saved by the heroic actions of a prince riding on a white horse.
But that is just something that is expected [of a hero in a game].
When a character is made as a hero, they are doing nothing more than demonstrating the ability and power given to them from the start.
So when a minor character (just a normal person) like the protagonist says something special to her even just once, she is happier than if the protagonist were a hero.
CCC is a story about the dignity of normal people.
To the AI Sakura, who could never be selected as a heroine, this dignity is true beauty, and the expression of this dignity is like a precious miracle to her.
That’s why she ran. 38,000 light years into the darkness.
…So that even if this dignity disappeared at the end of the Holy Grail War, it’s afterimage would still remain for a time.

Fate/EXTRA Material: Encyclopedia of Fate/EXTRA