There's quite a bit of stuff in Christianity that isn't in the Bible that is accepted as dogma.
Abortion isn't in the Bible. There are rules about striking a pregnant woman in the belly so that she miscarries, but there's nothing specifically in there about deliberately aborting a pregnancy, other than the umbrella "Thou shalt not kill".
There's nothing about celibacy for priests.
Nothing about intercessory prayer to Mary the mother of Jesus, or to various saints.
Nothing about saints, either, come to that. The idea that certain holier-than-others people, upon dying, become capable of engineering miracles upon request is not in the Bible.
Nothing that directly and clearly stipulates whether Jesus is in fact coming back to Planet Earth at some point, and if so, when, and how. The various prophecies--Revelations, etc.--all have numerous different and frequently diametrically opposed interpretations even in mainstream Christianity.
Nothing that establishes a Pope.
Ditto for infant baptism. Baptism in the New Testament is something undertaken by new believers as a public confession of faith. It's symbolic of their new life, now that they have chosen to follow Jesus--the old life washes away, the new life begins. The idea that newborn infants must be baptised to save their souls from eternal damnation isn't in the Bible anywhere.
Nothing about Purgatory, a place where the dead go to pay some dues before they can be allowed into Heaven.
Nothing specific about what happens to your soul when you die. Are you asleep until the Last Trump, or do you go straight up to the Pearly Gates and mingle until the Last Trump? It depends on who you ask (see above, Revelations).
So, to answer your question about SSM and the Bible...it's all just tradition. Dogma. Homosexuals are condemned in the Bible as perverts, therefore two homosexuals marrying would be, like, 2x as perverted. Personally I always thought, "If they're already going to Hell anyway just for being homosexual, why not let them go ahead and compound their error by getting married? Then they'd be, like, 2x damned!" But logic is of no use here.