Is ablution valid if the one performing it says "Bismillah" at the beginning and then again when washing the feet?

Saying "Bismillah" at the beginning of ablution (wudu') is recommended by the majority of scholars. As for the remembrances (adhkar) of ablution that are recited during it, they are fabricated falsehoods; nothing of the sort has been authentically transmitted from the Prophet (peace be upon him) except for saying "Bismillah" at the beginning, and saying: "I bear witness that there is no god but Allah alone, without any partner, and I bear witness that Muhammad is His servant and Messenger. O Allah, make me among those who repent, and make me among those who purify themselves" at its end. In Sunan An-Nasa'i, the following is added: "Glorified are You, O Allah, and praised be You. I bear witness that there is no god but You. I seek Your forgiveness and repent to You." Therefore, supplicating during ablution is not legislated, but it does not invalidate it.