The only three shirabyoshi who are really popular and well-known are:
1. Gio & Hotoke from Tale of the Heike (Kiyomori released Gio from his patronage and left her for dead after he saw Hotoke dance, later Hotoke felt the same thing would happen to her and joined Gio in becoming a nun).
2. Shizuka, who was supposedly a wife or concubine of the great general Minamoto Yoshitsune, also of Tale of the Heike fame. He was on the run from his brother Yoritomo, who saw him as a threat to the Kamakura shogunate's throne and wanted him and his entire line eradicated, so Yoshitsune left her in the Yoshino mountains, where she was eventually captured by Yoritomo and made to dance for him...later he killed her newborn son. Or so the story goes.
I essentially have to prove the historicity of these two. The only lead I have for Shizuka so far is that all of the stories about her corroborate at major points, which means there is a national idea of her story being 'a certain way', which is good evidence for actual historicity.
Gio and Hotoke, on the other hand, are a little more difficult. The only thing I've managed to dig up is
Gio-ji, a Shingon temple in Kyoto which is supposedly where Gio and Hotoke lived as nuns. It claims to host Gio and her mother's graves, which would imply actual existence. However, it's also quite possible that it's a grave only in spirit, since Gio is a celebrated and famous figure in Japanese history.