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.
The heart is the place of intention, so you are not obliged; rather, you are not permitted to pronounce it. It is sufficient for you to have the intention in your heart without moving your tongue that you are performing Ghusl (ritual bath) for the prayer or to remove the ritual impurity, and say Bismillah, at the beginning of Ghusl as you say at the beginning of ablution. However, if you are performing Ghusl in a washroom, then you should say Bismillah before entering it.
We ask Allaah to facilitate every good for you and us.
Allaah Knows best.