The majority of scholars (Hanafis, Malikis and Shafi'is) hold that saying "Bismillah" at the start of wudu is a strongly recommended sunnah, while the Hanbalis and Shaykh al-Islam Ibn Taymiyyah held it obligatory upon one who remembers it. Their evidence is the hadith "There is no wudu for the one who does not mention the name of Allah over it," reported by Abu Dawud (101), at-Tirmidhi (25) and Ibn Majah (399), which some scholars graded hasan or sahih by its supporting routes and others graded weak. Since the wudu verse itself (Quran 5:6) mentions only the washing and wiping of the limbs, the safest practice is to always say Bismillah, and if you genuinely forget, your wudu is valid by the agreement of the majority. Say it at the beginning, or whenever you remember during the wudu.
Q&A · Purification
Do I have to say "Bismillah" before making wudu?
Evidence — the daleel
On deen2u
Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.