This question conjures up different feelings in different people. I came out of a background that included people who made notes in their Bibles, so I have never considered that it might not be okay. However, a few people think you should not, and others who do not consider it inherently wrong do not feel comfortable marking in their own Bibles.
A small minority cite verses such as Deuteronomy 4:2, Proverbs 30:6, and Revelation 22:18. These verses warn against adding to the word of God. Those who cite these kind of verses would charge those who make notes with adding to the word of God. Contextually, these warn against making men’s words equal to God’s words, with an authority that is unwarranted. Jesus makes the case against this in Mark 7:7-13, as well as other places. This has nothing to do with writing in or on a physical or material element such as a scroll or book.
I mark up my Bible (singular). That is, I mark the one I am continually reading and studying. I do not mark other Bibles that I just use for reference. I use a wide-margin Bible, making notes with pen & highlighting. I do not feel uncomfortable doing so. Some may feel disrespectful or “weird” writing in their Bibles. Others like to keep all their books as clean and pristine as possible, and include their Bibles in this preference.
God’s word should be in our mouths (Joshua 1:8), our minds (Hebrews 8:10), and our hearts (Psalm 119:11). The word should be consistently and constantly before us (Deuteronomy 6:6-9; Proverbs 7:2-3). To the extent that writing in a material Bible helps with that, it is a good thing. Making notes in a Bible usually helps you remember what you have read, see what is there, and find it more easily when looking for it again.[i] The Bible is the inspired and inerrant word of God. Never challenge or change it. The book itself is paper and ink. Certainly, treat it with reverence and respect for what it contains. Nevertheless, adding more ink or some highlighting will not destroy God’s word – and just might help you “search the scriptures” and to “study to shew thyself approved.” For those who prefer not to write in their Bibles, they might receive the same benefit of help and memorization by using a notebook. A journal on paper or on the computer should serve the purpose.[ii]
I am not aware of any scriptural teaching or principle that requires that a paper and ink printing of the word of God must be kept pristine. It seems that it is okay to write in the Bible if you are not trying to write a Bible!
[i] One negative is that the notes (the second time around) might keep a person focusing on the same scriptures to the exclusion of other scriptures that aren’t “noted.” Another positive of marking in a Bible is that it becomes a meaningful treasure when passing down to children or grandchildren.
[ii] There are Bibles with blank pages for writing, which might serve as a compromise between writing in or not writing in the Bible.