You wouldn't want to connect the BD directly to a bio filter, waste just collects and clogs it.
It sounds like the BD goes into the skimmer basket? If it was working the best it would do is collect string algae, leaves. That's nice, but not super important. A proper BD system removes more important waste like fish poo. But most Water Gardens don't need that with their small fish loads and light feeding.
Yes, a BD is easier to run when it has it's own pump, but not connected directly. Your BD could be clogged. One of the problems with skimmer/BD on one pump is there is enough flow to pull crap into the drain but not enough to pull the heavier stuff up the pipe so it collects in the pipe and clogs it.
So for the bio balls the easiest thing is to add another pump and just pump into the container of bio balls and have that drain back into the pond and Bob's your uncle.
Not sure if you're planning to have the bio balls submerged or above the water so water just flows over them, called a Trickle Tower. But the Trickle Tower scheme has some pluses. Tested to convert 30 times more ammonia than submerged because of increased O2. And TTs do that 24/7 because it never has to be cleaned. Heck, not having to clean is a big plus in my book too. Performance of submerge drops off as muck dust settles on the media. So you could buy a lot fewer bio balls and get the same performance. Plus a TT of bio balls weighs a lot less than a container full of water so mounting can be easier.
Skimmer --> pump -> bio is pretty standard if you wanted to redo plumbing. So that probably means cutting the pipe coming out of the pump (and goes back to the pond) and hooking the bio in there. But I'd need a diagram of your set up to know. In this case I'd plug the pipe in the skimmer that goes to the BD. Doesn't sound like it's doing anything for you anyway.
