When is she eager to turn you? Every time I asked her she was reluctant. Saying something close to - " Are you sure? This isn't like changing a pair of clothes, once you do this there's no going back. "
Just some random comments when you take her to places and when you talk to her to give her items akin like when she says
"This place is beautiful, I'm glad you are here with me."
Also knowing you are a Vampire Hunter she still offers to turn you into a Vampire knowing you are gonna' say no, in the quests and even after.
Just little subtle things you notice when you do the quests.
Shes a corrupter of men.
Many theories have surfaced about why she is infatuated with the dragonborn from the moment she is set free but my explanation is..
When the spike stabs your hand and the blood leaks into her tomb and you set her free it was the first taste of blood shes had in 4000+ years so to her the only way she can repay you for such "kindness" even though you didn't initially mean to set her free is to give you the highest gift and honor she can give, vampirism.