I'm attracted to rides for many reasons, some of which are easier to put a finger on than others. If someone arranges words thoughtfully, it strikes me that she might do similarly with places, or people, or lines on a map. Which is as much as to say that I will be interested in coming on your ride if I like the cut of your jib.
I am an essentially shy person who likes people. Beer and bicycles are my preferred self-medication. Either will do, but both is ideal. I like cake, but am not quite as interested in it as some people seem to be.
The narrative is important, and it begins with the title. I don't like soap operas, so I tend not to be drawn to rides, or threads, whose form keeps them alive long after they have been emptied of content.
@iLB won me over instantly with a title. London Beer & Bridges Ride has four selling points in five words. The Friday Night Ride to the Coast was an idea that enchanted me long before I got round to doing the ride itself.
Rides don't have to start at Hyde Park Corner, The Wales Millennium Centre or York Minster, but they really should
never start at the McDonalds car park in Briton Ferry. And I say that with the greatest affection for Swansea CTC.
I like the abdication of responsibility. I do a lot of exploratory riding on my own, equipped with Landrangers, and I tend to be the person who knows where we are and which way we are going next when riding with friends on my home turf. It is a great pleasure to show up with none of this responsibility, not necessarily knowing anything at all, and place myself in someone else's hands (this is related to the cut of jib thing above).
I'm a brisk rider judged by the pace of leisure cyclists, and a slow one judged by that of anyone with a training regime. I like to be pushed a little by faster riders, and obliged to take it easier by slower ones. A little bit of give and take on all sides, and a ride can comfortably accommodate a wide range of paces. Things that help this are a generous schedule, proper lunch stops, bailout options, a decent navigation system (the best, of course, is The Fridays' rolling waymarker/TEC combo) and well-thought out regrouping points. A large group waiting for the slowest rider at the top of every incline is going to make him feel rushed; whereas a stretch where everyone can ride at their own pace for five miles, then regroup and chat for a few minutes somewhere with a nice view or a chance to nip into a shop and buy a flapjack, will make everyone happier.
If you want particular people on your ride, invite them directly. Stating that no-one gets left behind is nice, but it isn't an invitation, and it won't allay the fears of someone who imagines they are holding everyone up, or fears that they won't fit in some other way. It's nice to be wanted.