Reference: Fataawa wa Ahkaam ilad-Daakhileen fil-Islaam – Page 25
Question: What is the ruling about he who recently embraced Islaam taking a bath? And is taking a bath a condition for the prayer, or is wudhoo [alone] sufficient?
Response: It is mentioned in the Musnad [of Imaam Ahmad] and the Sunan [of Abu Daawood] – on the authority of Qays ibn ‘Aasim that the Prophet (sal-Allaahu ‘alayhi wa sallam) commanded him to bathe in water and sidr (leaves from the lote tree). And in Saheeh al-Bukhaaree and Saheeh Muslim [it is mentioned] that when Thumaamah was ready to embrace Islaam, he went and had a bath, then returned and embraced Islaam. And [all of] this suggests that taking a bath was something well known for whoever wanted to embrace Islaam.
[In addition to this] the disbeliever is impure as Allaah has mentioned, and the one who is in a state of major ritual impurity whilst he is a disbeliever remains so even after he has had a bath; so because of this, Imaam Ahmad and others besides him are of the opinion that taking a bath [upon embracing Islaam] is obligatory, and no act of or worship – such as the salaah are correct until he takes a bath.