I think there is a misunderstanding here. A couple of them.
The Catholic Church does not teach that in order to get into Heaven you must know [Jesus] through [His] Mother.
She teaches that there are great benefits to invoking the Mother of God and teaches that God has entrusted every grace to her active intercession but there is no requirement for salvation that an individual, on their part, know Mary or asks for her intercession. Someone can be saved being entirely ignorant of Mary.
Another misunderstanding here is the idea that if something isn't in the Bible, it can't be a Christian teaching.
2 Thessalonians 2:15 says
- "Hold fast to the traditions you received, whether by word of mouth or by letter."
1 Corinthians 11:2 says
- "Now I praise you, brethren, that you remember me in all things and keep the traditions just as I delivered them to you."
1 Timothy 3:15 says
- "The pillar and foundation of the truth is [not Scripture, but] the Church."
The role of Mary is chiefly a matter of Christian Tradition, although we see hints of it in certain senses of Scripture, such as Psalm 45:9-17, where Mary is referred to mystically as the Queen of the King with the royal subjects seeking her intercession (In Near East societies, because of polygamy, the queen was usually the mother of the king, not the wife of the king).
There is much that can be said on this topic; if you want to read about the Scriptural and Traditional explanation for Marian teachings, I recommend the book:
Hope this helps!