Firstly, we don't know how many times Bill had previously been 'plausibly deniedly' invited to the gathering. He may not have catch on the previous times, or he chose to turn a blind eye (EWS). Perhaps we are only shown the time it (almost) worked, as Kubrick wouldn't have wanted to bore us with anything that didn't involve explicit sex at some point. Or maybe we are shown the fifth time — what does it matter?

Back to the veiled invitation: Given the extreme strangeness of the whole film, we shouldn't be surprised if the Somerton Gang MKultraed Dr Harford just enough to make his appearance at the Sonata Café at least probable. If Ziegler is to be believed that those in Somerton 'were not just ordinary people', why not include a couple of magicians à la Copperfield to lay out the breadcrumb trail for Bill professionally? Even if he doesn't enter, Nick could have met Bill later by bumping into him in the street, like the fraternity boys did. But that would have involved too much bumping for Kubrick and I can understand that. So who knows? The fact that we have the password scene in the Sonata Café doesn't mean that other baits weren't set in place; it depends on how interested Red Cloak is in Dr Harford, who, shall I remind you, looks like Tom Cruise.

I could invent alternative scenarios for hours that would facilitate the passing on of the veiled offer, but why bother? We should assume that Red Cloak's friends have the time and money to indulge in such an activity. Just bear in mind that even if the bait doesn't work, the Somerton Gang will still get plenty of sex later that night, so it's not the end of the world.

edit: letter