If the bottles weren't rinsed well from the cleaner, that won't improve. But, I'm not sure it's the cleaner any way.
Remember, that sanitizer is "no rinse" and you don't have to rinse it off. That kind of defeats the purpose of sanitizing. You shouldn't mix c-brite and campden, as there is no need to do that. Properly diluted campden (sulfite) solution is a very effective sanitizer.
One thing that comes to mind for me is something called "bottle shock". I'm not sure if this happens in cider, but it's common in wines. Sometimes just the act of bottling causes the wine to go "off" a bit. It's the movement of the wine and the racking and bottling. Within a month or two, though, it's much improved. Hopefully, this is what's happened in your cider. Try another bottle in two months, and I bet that it'll be much better!