Praise be to Allaah.
It is not obligatory for a woman to sit when doing ghusl, rather she may do ghusl however she wishes, standing, sitting or lying down. The same applies to men.
There is also nothing wrong with a person doing ghusl naked, as is explained in the answer to question no. 6894 and 6976.
Some fuqaha’ regarded it as mustahabb for a person not to stand when naked, when doing ghusl and otherwise; rather he should crouch so as to cover himself.
Ibn ‘Abd al-Barr (may Allaah have mercy on him) said: A man should not stand up straight when naked by night or by day. When he does ghusl he should crouch as much as possible, for Allaah is more deserving that he should feel shy before Him. End quote from Haashiyat al-‘Adawi ‘ala Sharh al-Risaalah (2/455).
This has to do with modesty and covering, but it is not obligatory.
And Allaah knows best.