Cycling is at least a form of exercise, and can reasonably be done alone; I suppose to make it enjoyable, you would need some actual trails and such near where you live...
Though you're likely to be judged and mocked the same behind your back for being a subhuman in such isolation, partaking in activities that are still often some with partners and friends, cycling allows you to escape any one who might lay an eye on you for more than a few seconds, as well as doing it alone being relatively more normal than other such activities; I doubt any fancy restaurants and such will find it normal for you to be dining alone, though.