Alright, gawdamnit, how do you invite them? This is really starting to **** me off. I want to upgrade my damn Swinging Sword and Tea Killer Shooter, damnit!
From what I can gather, you have to stand in their vicinity, but don't face them directly since that will highlight focus on them. I'm not sure if it interferes or not, but I think it does, because it seemed to me as if they stopped all other dialogue because they're curious and excited about what expressions you're going to do, like any NPC you highlight focus on ["this is going to be great!" etc.], so face away. Also, make extra sure that they're standing in their assigned spot. I've noticed that they had to be standing in a specific spot in order to be able to give sex invites. If they're not in their spot, simply wait in the area [again, don't face them] and eventually they'll walk back to it. When they're on "their spot", just wait in the vicinity until they make the offer. After that, you should be able to take them up on it by interacting with them. I had to be a bit patient with some of them.
PS. Off-topic but the male whores in Fable III look so ****ing stupid and repugnantly ugly, it's almost embarrassing to look at. Note that this is coming from a gay man.