Praise be to Allaah.
There is no specific duaa' for ghusl that is narrated in the Sunnah, but the majority of fuqaha' regarded it as mustahabb to say Bismillah when beginning ghusl, as is also the case with regard to wudoo', although there is no specific evidence for that with regard to ghusl.
Al-Maardaawi (may Allah have mercy on him) said:
It should be noted that the ruling on saying Bismillah when doing ghusl, as is done when doing wudoo', is a matter concerning which there is a difference of opinion. End quote from al-Insaaf (1/188).
It has previously been explained that the more correct opinion is that it is mustahabb to say Bismillah when doing wudoo' and ghusl. See the answer to question no. 83172.
And Allah knows best.