Can I put plasterboard in a general waste bin?

No, plasterboard cannot go in a general waste bin. Since 2009 gypsum has been banned from landfill with other waste, because it releases hydrogen sulphide when it rots alongside biodegradable material, so plasterboard must be kept separate from the rest of a site's waste and sent for gypsum recycling, where it is ground back into new board. That is why it is awkward and why collectors charge for it as its own stream: a mixed load with plasterboard in it is refused at the transfer station or re-sorted at your cost. Keep offcuts dry and bagged or stacked apart, and tell your collector how much there is. Its List of Waste code is 17 08 02.