All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
We have mentioned in Fatwa 82245 how the Prophet used to perform Ghusl (ritual bath), so please refer to it.
As regards having a bath while standing, we have not come across any text that prohibits this, as in principle all things are lawful unless there is an evidence which prohibits them, especially that it is difficult to wash some parts of the body while sitting, so there is no harm in performing Ghusl while standing.
Allaah Knows best.