Al-Nawawi narrated in al-Majmoo’ (1/385) that al-Bayhaqi said:

The soundest report concerning saying Bismillaah (for wudoo’) is the hadeeth of Anas, according to which the Prophet SALLALLAHU ‘ALAYHI WASALLAM put his hand in the vessel of water then he said: “Do wudoo’ in the name of Allaah.” [Anas] said: I saw the water springing up from between his fingers, and the people did wudoo’ until the last of them had done wudoo’, and there were nearly seventy men. Its isnaad is jayyid, and it was quoted as evidence by al-Bayhaqi in his book Ma’rifat al-Sunan wa’l-Athaar; he classed the other ahaadeeth as da’eef (weak). End quote.

With regard to what is said after wudoo’, a number of ahaadeeth have been narrated concerning that.

From the reports it may be concluded that he said:

Ashhadu an laa ilaaha ill-Allaah wahdahu laa shareeka lahu, wa ashhadu anna Muhammadan ‘abduhu was rasooluhu. Allaahumm aj’alni min al-tawwaabeena waj’alni min al-mutatahhireena, subhaanaka Allaahumma wa bi hamdika, ashhadu an laa ilaaha ill anta, astaghfiruka wa atoobu ilayka

(I bear witness that there is no god except Allaah alone, with no partner or associate, and I bear witness that Muhammad is His slave and Messenger. O Allaah, make me one of those who repent and make me one of those who purify themselves. Glory and praise be to You, O Allaah,  I bear witness that there is no god but You, I seek Your forgiveness and I repent to You).

Muslim (234) narrated from ‘Umar ibn al-Khattaab (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “There is no one among you who does wudoo; and does it well, then says, Ashhadu an laa ilaaha ill-Allaah wahdahu laa shareeka lah, wa ashhadu anna Muhammadan ‘abduhu was rasooluhu (I bear witness that there is no god except Allaah alone, with no partner or associate, and I bear witness that Muhammad is His slave and Messenger) but the eight gates of Paradise will be opened for him and he will enter through whichever one he wants.” Narrated by Muslim, 234.

Al-Tirmidhi (55) added: “Allaahumm aj’alni min al-tawwaabeena waj’alni min al-mutatahhireena (O Allaah, make me one of those who repent and make me one of those who purify themselves).”

Al-Albaani classed it as saheeh in Saheeh al-Tirmidhi. Ibn al-Qayyim stated in Zaad al-Ma’aad that it is proven to be from the Prophet SALLALLAHU ‘ALAYHI WASALLAM

With regard to the phrase “subhaanaka Allaahumma wa bi hamdika, ashhadu an laa ilaaha ill anta, astaghfiruka wa atoobu ilayka (Glory and praise be to You, O Allaah, I bear witness that there is no god but You, I seek Your forgiveness and I repent to You), this was narrated by al-Nasaa’i in ‘Aml al-Yawm wa’l-Laylah, and by al-Haakim in al-Mustadrak, from Abu Sa’eed al-Khudri (may Allaah be pleased with him). The narrators differed as to whether the hadeeth could be attributed to the Prophet SALLALLAHU ‘ALAYHI WASALLAM or whether these were the words of Abu Sa’eed (may Allaah be pleased with him).