I have a gruesome question...if he killed her in the bathroom with the box cutter then put her body in a recycle bin....wouldn't there have been a huge amout of blood not only in the bathroom but a trail of it to the bin?
Depends how careful he was. Cut her throat and let her bleed out over the toilet bowl, there would be minimal blood to clean up and most of it would be dealt with with a few bits of tissue and a flush.
It seems - from the story - that the bin was located in the bathroom.
Sorry - it is a horrific thing, but sometimes you have to think how to do it most effectively.