Ane knows the staff well enough that she knows of an out-of-the-way, upstairs office she can use that has a small mirror. She does not look like herself, and does not want have to explain if she does not have to, so she does not ask permission, leaving such explanations for is she is caught. She spends some time experimenting with the Disguise spell, trying to work out why it produced the face of her sister, and, more importantly, how to avoid that particular complication again in the future.
It would, maybe, be easier to test with Asha present, but she needs to rest and recover, apparently her spell really took it out of her.
Ane is curious about differences between their casting styles, and wants to do all sorts of experiments, but they discovered —when Ane came back from Thet with ideas about sharing spells between them— that Asha can't express her spells in terms of rote memorisable sequences and can not see how to implement the sequences Ane has written down. It was frustrating.