Observe the bike that you want to recycle. Does it appear to have any mold or overly dirty areas that make it unusable? Are there any sharp edges on it from wearing and tear or misuse? If those things happen to a bike, it sometimes is unsalvageable. There may be no way to recycle it except perhaps having it sold cheaply for reusable parts.
Consider whether you have any attachment to the bike. If it was a gift or perhaps is otherwise sentimental to you (perhaps you won your first race in it), you may want to hang on to it. If you opt to do that, you can still recycle it in a very cool way: repurpose it. Go to a fabric store and get a good, strong fabric. You may opt to hire a seamstress or simply buy seat cushion replacements to match a decor of a room in your house. Place it on a stand and use it as a stationery bike if it’s still in wheeling condition!
It’s only when a bike is in usable condition that it’s appropriate to recycle it, just as long as you have no extreme emotional attachment to the bicycle in question.