Asajj was not Dooku's apprentice. Especially not at every point in the series. She was his assassin. Sidious interpreted her as an apprentice and a threat.
Darth Maul was apprentice to Darth Sidious, then master to Savage Oppress. Darth Tyranus was apprentice to Darth Sidious. Savage Oppress was apprentice to Darth Tyranus, then Darth Maul.
Asajj was apprentice to no one.
Here's her official Star Wars databank entry.Dooku actually obeyed the Rule of Two, unlike literally every Sith we meet except Savage. Until Sidious forced him to betray Ventress. Dooku
very explicitly did
not take Asajj as his Sith apprentice.