Why must Catholics go to a priest to confess, and then do "penance"? I don't see it anywhere in the Bible. The Bible is THE authority on God"s requirents of His people.
The reason you don't see "penance" in the Bible is because of a difference in translation:
The ESV is translating the Greek word metanoeó which means, "to change one's mind or purpose." The Vulgate translated the same Greek word into Latin as paenitentiam agite (indicating doing or performing repentance or penitence), and the Douay Rheims translates that as "do penance." The Catholic practice of penance grew from this, and can be supported from other passages in the Bible, as seen in the accepted answer to a similar question.
Obviously, the Reformers rejected this practice based on their interpretation of the relevant texts, but ultimately, whether the word "penance" is "in the bible" comes down to interpretation.