Rabbeinu Yonah in Bava Basra 39a talks about someone who does Teshuva and calls him a Ben Teshuva. What is the earliest reference in history to the words Baal Teshuva? And why did it change from Ben Teshuva to Baal Teshuva?
There probably are more though.
As to why, the original is Baal Teshuva. So why did Rabenu Yona write Ben Teshuva is the real question, no?
The term clearly occurs all over Rambam's Laws of Teshuva. For instance in 2:1
הוא בעל תשובה גמורה
I don't know about earlier usages.
But Rambam's code played a very strong influence on a lot of how we name things, so it doesn't surprise me that it won out. (Another interesting one is the phrase "Korban Pesach" ["Passover sacrifice."]) In the Talmud it's just "the Pesach" and you have to realize it means the sacrifice. It appears a small handful of times in various less-authoritative midrashim; then Rambam started using it in his Commentary on the Mishnah; then codified Laws of the Korban Pesach (vs. Laws of Chametz & Matza), and the term's popularity exploded ever since.