Funnily enough I had the same problem when I was fishing in the Clarence River. The trick is to use the Catfish as the bait. Firstly, bream love it and secondly Catfish don't like to eat themselves.
I have no idea why it works, but I use it religously. When you catch the Catfish, kill it as quickly and safetly as possible. Then before you fillet the fish, grab a pair of pliars and rip out ALL the spines to reduce the possibility of any accidents.
Then fillet the fish and cut the fillet into strips and get to work catching those Bream!
Happy hunting!