Reference: Fataawa ash-Shaykh al-‘Allaamah Muhammad Naasiruddeen al-Albaanee fil-Madeenah wal-Imaaraat – Page 70
Question: Is it obligatory to utter bismillaah when taking a bath?
Response: Yes. Uttering bismillaah when taking a bath is obligatory, because the bath takes the place of the wudhoo, and [as is known] there is no wudhoo for the one who did not begin with uttering bismillaah.