pls correct me if I am wrong, for some Buddhist/Taoist, the
scrolls/statues are believed to house spiritual entity/ies in them,
hence the need to be 'disposed' of formally and properly (by
monks/priest).
Personally, to me a Bible is just a book (ok, it contain the
written word of God), and nothing spiritual about it. so there is
no need for a formal way to dispose it. by the way, I bought my
first study bible from a second hand bookshop when I was still a
student.
