| First, if you are out of warranty, the dealer is the LAST place that you want to go. They charge 3 to 4 times more to fix things.
It sounds to me like the pilot bearing is shot. This is a little bearing that guides the clutch plate assembly into position when you press the clutch pedal. Anyway, this can typically be repaired with a new clutch plate assembly and not a whole transmission. This would be my best guess as to your problem, but it could be a number of things.
I might be worth calling around to find a transmission specialist that can help you rather than letting MINI do it. | 
