Sayyidah Aishah Siddiqah (may Allah be pleased with her) narrates: When the Prophet (peace and blessings be upon him) got up for ablution, he would tip the vessel (and first wash his hands), say Bismillah, and then perform ablution thoroughly. Imam Abu Ya'la recorded this report, and Imam al-Bazzar recorded part of it: that when he (peace and blessings be upon him) began ablution, he would first say Bismillah. Both of these hadiths revolve around a narrator named Harithah bin Muhammad, on whose weakness the hadith scholars are agreed.
Hadith Referenceمجمع الزوائد ومنبع الفوائد / كتاب الطهارة / 1111