The reason for the common use of the three-letter acronym, בס"ד (BS"D), is probably because it does not contain the Hebrew letter Hei ('ה), that is used to imply the name of God, and for this reason, a page which contains the letters בס"ד (BS"D) without any other Torah content does not require Genizah (a process for writings that contain the name of God), and thus can be thrown away without a fear of desecration.
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The book "Toldot Yitzhak" (‘The Offspring of Isaac’), by Yitzhak Karo, Yosef Karo's uncle, offers the meaning of this custom of writing ב"ה (B"H), at the top of every letter, with accordance to the biblical verse: "In all thy ways acknowledge Him, and He will direct thy paths" (Book of Proverbs 3:6).