Where is the comparison to the apostles being priests in the Bible?
What you're really asking is, how does the authority Christ gave to forgive sins pass from the Apostles to priests? The following links provide a slew of scriptural proof texts as well as writings from Church Fathers that should more than answer your question. I earnestly hope that you'll read and prayerfully consider what they have to say.
Orders [Where do Priestly Orders Come From?]
Bishop, Priest, and Deacon
Why We Have a Ministerial Priesthood
Did Jesus Give Priests to the Church?
Since you are insistent on answers that only come from the written word of the Bible, my question to you is where does the Bible anywhere say one must hold only to the written word as the final authority on matters of faith?
I leave you with a suggested prayer, the "Those Nutty Catholics Couldn't Possibly Be Right, Could They? Prayer ":
Dear Lord, I want to make it clear upfront that I don't believe that those misguided, sometimes nutty (but always lovable) Catholics could possibly be right in what they assert to be the Truth. But on the infinitesimally small chance that just maybe the Catholic Church is in fact what she claims to be, namely the Church founded by Your Son and my Savior, I freely open my will to your Divine guidance and ask you to lead me to the truth about the Catholic faith. The pursuit of the fullness of Truth is my only desire, Lord, no matter where it may lead. It goes without saying that I know it can't possibly lead to Rome ... but, Lord, I promise to follow wherever you lead me.
God bless you, friend.