All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah and that Muhammad, is His slave and Messenger.
Saying "Bismillaah" in Wudhoo' (ablution), Ghusl (ritual bath) and Tayammum (dry ablution) is obligatory according to the view of Hanbalis. According to their view, saying "Bismillaah" is only obligatory at the beginning of a worship and it is not obligatory to repeat it afterwards. So, by saying "Bismillaah" at the beginning of the obligatory Ghusl, you have fulfilled what is obligatory and you do not have to repeat "Bismillaah" when washing the body parts that must be washed during ablution. This is because those parts are included in the whole body that is obligatory to be washed when performing Ghusl.
Allah Knows best.