In Vancouver BC, new or used drywall can be disposed of at a number of locations.
One option with new or used drywall pieces is to take it to Vancouver South Transfer Station or Vancouver Landfill. With used drywall you have to double-bag it and seal it in plastic bags that are 6 mil thick. There are some quantity limitations, you can double check details at city of Vancouver website.
Another option with new or used drywall disposal is North Shore Recycling & Waste Centre which accept bigger quantities of new drywall. Again with used drywall it needs to be double-bagged and sealed in plastic bags that are 6 mil thick. You can check details on their website. You can buy those used drywall bags at Lowes (2727 E 12th Ave).
Yet another way to dispose new or used drywall is New West Gypsum Recycling. Used drywall must have visible date stamp not older than 1990.
Good luck.