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
Sayyiduna Abu Hurayrah narrates: The Prophet (peace and blessings be upon him) said: "O Abu Hurayrah! When you perform ablution, say 'Bismillah wal-hamdu lillah' (In the name of Allah, and all praise is for Allah); your guardian angels will keep recording good deeds for you until that ablution of yours is broken."
Imam al-Tabarani recorded this report in al-Mu'jam al-Saghir, and its chain is hasan (good).
Hadith Referenceمجمع الزوائد ومنبع الفوائد / كتاب الطهارة / 1112