Which adhesives work well when gluing vinyl to plastic?
I recommend using plumbing silicon (not acrylic) from a tube, the kind that is used to seal the gap between a sink and porcelain tiles. It will remain flexible and if you spread it evenly it will stick pretty much forever. It is also quite cheap and waterproof - one tube should be enough for you. 

Lay your vinyl sheet on the bin, mark it and cut it to shape before you glue. Press out long lines on your bin, smear them flat with a tool and place the middle of your sheet on the bin - working outwards. Let cure for 24 hours.