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.
It is not forbidden for a person –whether a man or a woman –who performs Ghusl (a ritual bath), to bath while standing if he/she is safe from other people looking at him/her. Moreover, we are not aware of any evidence from the Book of Allaah or the Sunnah of the Prophet that proves that this way of performing Ghusl is forbidden and no scholar has ever said that it is forbidden.
In addition to this, performing Ghusl according to the Sunnah is not an obligation but it is desirable. If a person performs the sufficient Ghusl without observing the Sunnah, he will be rewarded for doing so, Allaah willing, but he misses the reward of performing the desirable acts. It is also hoped that he will get the forgiveness that is mentioned in the saying of the Prophet : "Whoever performs Ghusl on Friday as best as he can and applies perfume on his body and then goes (to the mosque) without separating between two (sitting persons) and prays as much as he wishes, and then when the Imaam comes he listens, his sins between the two Fridays will be forgiven."
For more benefit, please refer to Fataawa 82245 and 83895 on the sufficient method and the Sunnah method of performing Ghusl.
Allaah Knows best.