Interesting... I had never heard of such "black belt clubs" before. I guess they must be more popular on the other side of the Atlantic; I don't think we have them over here.
Among the "schools" I've attended over the seven short years my martial instruction has been going on for, the current one is probably the one with the closest thing to a "BB club".
With my very first instructor (Japanese), there was zero fee involved. He taught for the sake of it, and classes would take place in a public park.
My second instructor's dojo ((British) would offer the choice of paying on a per class basis (the choice I had to go with, not knowing for how long I'd be staying in town) or through an annual fee. It was pretty McDojo-ish (expensive, lots of extras to be had for a fee, belt-mill-like superfast gradings and the obviously-lacking black belts that come with it, birthday parties for kids, etc.) but the instructor was extremely competent and I loved what I learnt there. I still practice some of it to this day, even though I no longer do jujutsu.
My iaido instructor teaches for the sake of the art. The annual fee is approximately $40, which is but the price of the federation license stamp. The training facility is kindly lent by the city.
My Chinese instructor in Tianjin (a highly traditional type) would charge a fixed fee (can't recall how much that was) for a 20-class package. The student was absolutely free to make those 20 tuitions last three weeks by showing up every day (I did), half a year by showing up once a week, or twenty years by showing up once a year if he so desired. The fee was for the instructor's time, as training would take place in a public park (pretty common practice over there), but he was definitely not stingy with the said time: although classes were meant to end at 6 PM, they would often stretch to 8 or more if the students were willing to go on (I was). One last detail: that fee only applied to European barbarians. Chinese could be instructed for free, and Japanese devils would be barred from it altogether. That's China for you!
My current instructor (Chinese-Vietnamese) charges an annual fee. The fee varies depending on whether you choose to attend one class a week, two classes a week, or all weekly classes. The club doesn't own the training facility but rents it on a per-hour basis, so the charging system makes sense. Yet I guess you could call the one-class-a-week program a "basic" package while calling the higher intensity ones "black belt clubs", it's a mere matter of vocabulary here.