Is placing a paper written on top of a book on which "Bismillah" is written considered a desecration that necessitates disbelief, and is the one who hands the pen in this case considered a disbeliever?

There is no harm in a writer relying on a book that contains the name of Allah the Almighty. This does not constitute a desecration of the Glorious Name, nor does it make the one who does it, or assists in it, an infidel. It is advisable to turn away from such whisperings (waswas).