Last time I heard they have about 900 in the collection, but they keep about 500-600 on display at any one time. On the first floor is the restoration facility (you can see it from the upper floors, they're the dark pictures). They only allow the public down there on special occasions so I've only been down there once. What you can't see from the upper floors is the "holding room" where the bikes that are awaiting restoration are kept, stacked on shelves like groceries. The whole place is quite a site to behold.
If you have access to the latest issue of Motorcyclist magazine there's lots of neat pictures from Barbers. I was there the weekend before the whole crew from Motorcyclist got there, but I did get to meet Brian Catterson (used to write for Cycle World, now for Motorcyclist). He said he was thinking about moving to Birmingham because, "the houses are cheap and you've got Barber's right here...what more could I ask for?"
Motorcyclist said that if you live within 1000 miles it's worth it to go...I think it's worth visiting from anywhere.