Solo cyclist here, also. I always have ridden alone, it wouldn't actually occur to me to ask anyone to join me, but then I don't have any friends, so...
The only time I ever actually rode regularly with anyone was commuting to work by bike way back in the late seventies-eighties, but we were riding to work, what was there to talk about?
All I really do is pootle around. There used to be a couple of older guys around here who did the same, you'd see them now and again, just out and about, going nowhere special, doing nothing in particular. Haven't seen them for years so they must have popped off. I could be the local, old, cycling weirdo these days, but that's ok.
If anyone wants to form an anti-social cycling club I'd be up for that, we could all arrange to meet somewhere then none of us would turn up, it'd be great!
Happy cycling everyone, however you do it.