With thanks to Malka, who taught this to me
In spite of his piety, Jesse was not always proof against temptation. One of his slaves caught his fancy, and he would have entered into illicit relations with her, had his wife, Nazbat, the daughter of Adiel, not frustrated the plan. She disguised herself as the slave, and Jesse, deceived by the ruse, met his own wife. The child borne by Nazbat was given out as the son of the freed slave, so that the father might not discover the deception practiced upon him. This child was David.
~Legends of the Jews by Louis Ginzberg, page 911
Source: An unknown Midrash quoted by Makiri, Ps. 118, 214. On the references to this legend by the medieval authors, see Zunz, Synagogale Poesie, 129. Comp, also Kele Yakar, 1 Sam. 17; Azulai, Midbar Kedemot, s. v. Yishai, No 20; R' Elijah Wilna in his commentary on Yoreh De'ah 157.24. Comp. note 23. Josephus, Antiqui, XII, 4.6, narrates a similar story about Hyrcanus the son of Joseph the tax collector. As to the names of Nazbat and Adiel (which occur only in Baba Batra 91a), see Gudermann, Religiousgeschichtliche Studien, 49, seq. The reading Adael and Ada instead of Adiel are incorrect; see 1 Chron. 27.25 where a son of Adiel is mentioned as King David's treasurer.
Compare to: Tamar deceiving Judah, Rebecca deceiving Isaac by covering Jacob in the hairy goatskins, Leah deceiving Jacob, the story of Shulamit who slept with the Egyptian because she thought it was her husband, loads of fairytales and mythological tales in various forms (Uther taking the form of Gorlois, Siguror and Gunnar in the Brynhild story), Sanhedrin 75a