Shaykh Muhammad Ibn Abdullaah Baa Jammaal was asked:
“Is it permissible to do Wudu inside the washroom knowing that he will say bismillah at the start of the wudu?”
“No problem with saying Bismillah, and saying Bismillah according to the correct stance of the people of knowledge is not a condition. Rather, it is recommended and an emphasized Sunnah. It is possible one leaves it off. Along with this, the people of knowledge say the remembrance of Allah in the washroom is not permissible at the time of relieving oneself. As for if he has finished relieving himself and distanced himself [from the toilet], and wants to make ablution, then there is no problem with this. This is the verdict of Al Allamah Al Albaani, and our Shaykh Al Allamah Al Waadiee as is found in Ijaabatus Saail.” End translation.
Majid Jawed Al-Afghanee