There is no specific du‘a for ghusl that is narrated in the sunnah (prophetic teachings), but the majority of fuqaha (jurists) regarded it as mustahab (desirable) to say bismillah (in the name of Allah) when beginning ghusl, as is also the case with regard to wudu (ablution), although there is no specific evidence for that with regard to ghusl. 

Al-Mardawi (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 wudu, is a matter concerning which there is a difference of opinion. End quote from al-Insaf.

It has previously been explained that the more correct opinion is that it is mustahab to say bismillah when doing wudu’ and ghusl. See the answer to question no. 83172. 

And Allah knows best.