I think I see a Floyd Rose licensing mention on the bass side, so my guess would be that it's just an 'in house' BC Rich copy of an "original" (as in, no fine tuners) Floyd Rose? Is it the guitar recessed underneath where that came from?
It's not recessed. It's a model, like the one here:is popular for but there's a million companies making similar. The Wilkinson I linked is a pretty good example, in that they have one arced and one flat 'knife edge', so that they can work with a variety of stud spacings; you'll see that same setup on other aftermarket bridges in the style you should be after.