No matter how you do dispose of it, you absolutely should not dump it at a place that is not designated for garbage disposal. Not only does this leaving the landscape look terrible, but in most parts of the country it is absolutely illegal. Almost every jurisdiction has rules against dumping, and if caught, it can come with some very serious fines. With enough research, you should definitely be able to find away to safely and responsibly remove the bed from your home.
When considering whether or not you can recycle it, you should keep the three “R’s” in mind. These are reduce, reuse, recycle. So first consider whether or not you really have used it to the end of its life. If so, take the time to see if there might be someone else that can put it to use. If there isn’t, then it is definitely time to looking into the option of recycling.