Two theories on the popularity of the Bicentennial (into whose production went perhaps the least love, they didn't even have gut bevelling!):
1. They came out when TBirds were - for the first time - regarded cool (unlike the sixties where they met indifference of the public). Name players such as Tom Hamilton, Steve Priest, Roger Glover, Jackie Fox, Phil Way played them from 1976/77 onwards (for a while at least) and you suddenly saw more TBs than ever before. Gibson quickly followed the trend by bringing out the RD basses which to all intents and purposes were TBird shapes sans neck thru (too expensive), long headstock (too frail and neck-heavy), but with a cutaway (better high register access).
2. As mentioned before, there is an inconsistency/variance between various specimen that makes them attractive to collectors - in contrast any two post 87 modern Birds will sound pretty much the same. Even when playing one Bicentennial specimen only, the bass very much reacts how hard you play, there is a lot of compression and distortion going on with those Bicentennial pups and some people find that responsive and raunchy, others prefer the "no matter how hard I play, the bass' signal is consistent" approach of the TB Plus pups of the modern TBirds which also have more low frequency ooomph (while the Bicentennials and sixties models have more of an overdriven rrring to them).
Uwe