Bible doesn't explicitly mention masturbation anywhere. Usual souce of this prohibition is the sin of Onan. Unfortunately, that wasn't masturbation. Onan was having sex with his wife and withdrawing before climax so as not to get her pregnant. That's not masturbation.
And the Jewish arguement about not wasting one's seed (semen) while actually a lot clsoer to the act of masturbation falls apart with the use of the word "waste." Masturbation doesn't waste one's seed but actually strengthens it making sperm 'better swimmers.' Then there's the laundry list of health and psychological benefits to the deed. If anything's it's exercising your reproductive system. Makes you healthier, saner (less horny and motivated by lust,) and better at the act of sex teaching you how to recognize impending climaxes so you can last longer and get your partner off first.
If a religion teaches something with objective health benefits which does all good things and no bad things is a sin, then that religion isn't a religion but a cult.
Considering plenty of cults use and have used the Bible only method, your last point is fatally undermined. The Bible is not and never has been the sole rule of faith. Jesus promised the Spirit of Truth to guide his Church into all truth. He commissioned his apostles with his own authority instructing them to teach the nations, to baptize, to forgive sins, to bind, to loose, and to receive the Holy Spirit directly. Nothing Jesus did even hints that they be bound by a book.......which wouldn't even be made official until 4 centuries later. Even that event, where the Church of God decided what is and isn't the Bible is certain proof of where the real authority is both then and today.
I don't care if it's in the Bible or not. Christ's Church says masturbation is a sin. Therefore it is.