I want to know how people know that the Holy Quran expects its readers to know the Holy Bible.
One such claim is
"The Quran assumes familiarity with major narratives recounted in the Jewish and Christian scriptures."
Ref.: en.wikipedia.org/wiki/Quran
The Wikipedia page you referred to in comment, somewhat answers your question. Relevant lines from Wikipedia are
"The Quran assumes familiarity with major narratives recounted in the Jewish and Christian scriptures. It summarizes some, dwells at length on others and, in some cases, presents alternative accounts and interpretations of events.[12][13][14]"
Above statement has three references, two of which appear to be books and third is verse of Quran. You can look for those books. As for the verse of Quran, it is
"Say: 'We believe in God, and that which has been sent down on us, and sent down on Abraham and Ishmael, Isaac and Jacob, and the Tribes, and in that which was given to Moses and Jesus, and the Prophets, of their Lord; we make no division between any of them, and to Him we surrender.'"
The wiki paragraph, uses words "assumes familiarity", but that 'familiarity' is only related to Jews and Christians, because they believe in those narratives but have misunderstandings/misinterpretations and corrupted data. For others, those narratives are just a new set of knowledge.
That verse shows that Muslims are required to recognize the books/scriptures given to other prophets as word of God, among which is Bible. But since it is believed to have been corrupted, so they are not required to read that. It is like, when there is a new version then you are not required to read the outdated( and/or corrupted) version.
Here is an other link related to Islamic view of Bible. This link states(with references) that Muslims are required to believe that Bible was divine, but are also told that Bible is now corrupted. So, Muslims are directed to only take guidance from Quran. This page also mentions
"Abu Hurairah, a companion of the Islamic prophet Muhammad had narrated, "The people of the Scripture (Jews) used to recite the Torah in Hebrew and they used to explain it in Arabic to the Muslims. On that Allah's Messenger (ﷺ) said, "Do not believe the people of the Scripture or disbelieve them, but say:-- "We believe in Allah and what is revealed to us.""
Summary: Quran does not expect its readers to have read Bible, but expects Christians(who have read Bible) to read the Quran.
It does not assume one to know the Bible by any way. But what it says is those who've read Bible(True Bible like Old Testament) find the same flavor even in the Qur'an, and also most of Qur'aninc verses confirm what's there in Bible(I mean the True Bible like Old Testament (or) the words of God aggregated in the Bible) abrogating a few.
May the creator guide us all.
