The Catholic Church has dozens of ritualistic practices that are very specific in how they are performed and why they are done. Virtually none of them are outlined in the bible even if there is a line or two that they use to justify why they perform them. For instance, the priesthood is supposed to remain celibate, the existence of the Pope and how the Pope is selected. The entire structure of the priesthood. Infant baptism, something that I have thus far not been able to locate in the bible but is considered an obligation under Catholic doctrine. Praying to (or as a Catholic might say petitioning) the saints which certainly is not in the bible and an argument can be made that it is antithetical to the bible. The very existence of the Catechism itself. It only exists to outline those things that are traditional or interpretive rather than directly spelled out in the text.
Busy week, got distracted. You say that there is no Biblical reason for this.
Jesus was celibate. He noted, Some are born eunuchs; some are made eunuchs; and some become eunuchs for the sake of the Kingdom of God. Those are the Biblical reasons for a celibate priesthood. In addition, there was a practical reason of what belongs to Church, what belongs to family.
Biblical: Jesus noted that Peter and Peter's faith was the rock on which the Church was to be built. In early Christianity, the Bishop of Rome was known as "Papa" which over the years changed to Pope. Papa is the head of a family. Jesus and the Apostles spoke of spiritual fathers.
Infant baptism: Entire families were baptized. And that tradition continued as a baby is not outside the family, but included with everything inside the family. The same is true with the Body of Christ. "Let the little children come to me."
Both the living and those who have passed on are the Body of Christ. (As Jesus said, God is God of the living.) And, where two or more are gathered in his name, so is he. Asking a saint who has passed on to join in prayer is no different from asking a friend or family member praying beside to pray with/for us.
Have you ever looked at the multitude of footnotes in the Catechism of the Catholic Church. Biblical references.
So there you have it. You also have Paul saying, Those who can take it should, but those who cannot should marry. Therefore, I have no quarrel with non-Catholic ministers who marry. That is Biblical as well.
Again, the Catholic Church is quite Biblical, even more so than many non-Catholic denominations. However, it is not the point of the Bible to sent up a contest on who can do more. As you can see from what I pointed out, the Bible often covers different options.
So once again, what is non-Biblical about Catholic practices? The question is rhetorical. Catholics are quite Biblical, even more than non-Catholic denominations who give little attention to the Old Testament.