@wafter I've some experience as a current club sec and someone who has tried to help friends in dark places.
If you were to join my club and suggest a new ride you would be encouraged and supported to do it. I would expect any good club you find to be the same. For most clubs finding people prepared to do something and help out is a major challenge. Do consider it.
If you choose to organise your own informal group I would advise against Ride Leader courses/qualifications. It's a minefield and uneccessary. I suggest all you need do is make clear self-sufficiency is important - tube, patches, pump - and a helmet strongly advised. Beyond that it's simply meet at 9.00 Saturday for a couple of hours ride and chat.
As for selling the idea and getting the message across something on the lines of "life can be very difficult for some, a chance to clear the mind, chat with others, forget daily challenges and enjoy the fresh air" might be a starting point.
As I said I have supported people in the past. It was one of the emotionally difficult and draining things I have ever done. Be sure to care for yourself first. It is hugely rewarding though to see friends come out the other side with new lives. For my trouble I gained one very close and dear friend who will be with me for life. A thing to cherish.