Is it permissible to enter the bathroom with the Holy Quran that I place in my book bag, knowing that I fear it will be stolen if I leave it outside the bathroom?

If it is possible to keep the Mus'haf (Qur'an) outside the restroom, that is better. However, if there is a concern about it being stolen or lost, then there is no harm in bringing it inside a bag, while keeping it as far as possible from the toilet.