Look after your garden and buy a shredder. Put through it anything that won’t naturally breakdown quickly and then add it to your compost or use directly as mulch on your garden.
Let’s think about the alternative – plants grow in your garden using nutrients from the soil, they die or you cut them down and put them in your green waste bin. A man then drives around town in a truck to take your plants somewhere else where they’ll rot. Why not let them rot at home where they can help your garden grow? Abandon your green waste bin for ever and buy a mulcher!