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Your point is worth emphasizing: Scripture doesn’t teach this doctrine of “the Bible alone” as the sole rule of Christian Faith. Indeed, the Bible points to a magisterium, founded on the apostles and their teaching (Acts 2:42, 1 Tim. 3:15) as well as Sacred Tradition (2 Tim. 2:2).
In addition, the assertion of sola scriptura is self-refuting. That is, it requires an authority outside of the sacred pages to make that determination. It would require at least a God-ordained magisterium. Indeed, the early and most influential Protestant Reformers—Martin Luther and John Calvin—undermined their own “Scripture alone” claims when they realized that they would have to teach their interpretation of Scripture as authoritative over and against someone else’s, including each other’s.
For more on sola scriptura, see this Catholic Answers tract and this Catholic Answers Magazine article.