Did Caleb’s son Mered (I Chronicles 4:18) marry the daughter of Pharaoh mentioned in Exodus 2:5-9

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I recently stumbled upon a statement of 1 Chronicles 4:18
indicating that Caleb’s son Mered married a daughter of Pharaoh named Bethiah, who bore him three sons.

Mered’s Egyptian wife bore Jered, the father of Gedor, Heber, the
father of Soco, and Jekuthiel, the father of Zanoah. These were the
sons of Bithiah, the daughter of Pharaoh, whom Mered married.

Is Bithiah the same woman who rescued Moses from the Nile in Exodus 2:5-9? I see that rabbinical tradition answers yes, and includes one report that she took this name (which means "daughter of YHWH") because she was a convert to Israelite religion. I am wondering if there are any biblical clues or opinions of the Church Fathers that support the fact of Bithiah being the same Egyptian princess mentioned in Ex. 2.