Bass and Bluegill are simply not as smart as carp. Bass in particular are ambush predators, and more important than imitating their exact forage is triggering the predatory instinct. Bluegill basically eat, or try to eat anything. It could still be true that a fly that works in one pond for those two would also work for carp, but it doesn't HAVE to be true. I personally think knowing the forage is crucial, so I spent a lot of time figuring that out. I would go to areas where carp feed and watch them, dig in the bottom to see what was there etc. I started catching more carp when I paid attention to this, and I started catching a LOT of carp when I figured out that their primary forage was clams. That bit of information not only affected my fly selection, but more importantly HOW i fish all my flies. In short, they don't have to chase clams, so I don't make them chase. San Juan worms and various nymph patterns are likely to work on any fish out here if presented properly to a feeding fish.
My four main rules that I follow to catch carp on the fly:
1) Know your forage
2) Don't cast until you can see the head
3) You gotta make 'em move (you want them to turn to the fly so you can set the hook when you see the head turn)
4) To catch more carp...cast at less (you want to cast at feeding carp...not waste time or risk spooking a non feeding fish that will spook the feeding fish)