Bull sharks seasonally migrate south during January. You will not find a bull shark smaller than 2.5 metres or larger than 3.5 metres south of the manning river. It's a little complicated although the rivers will hold baby Bull sharks north of the manning river and then the larger models starting at 2.4m begin migrating too and from Queensland and the NSW coast as far south as Montague island and rivers around there, I think they become rarer after Batemans Bay. Adult bull sharks live in water above 22 degrees although colder water will not kill them. The smaller ones do not migrate with warm water but this also explains why they only live as far south as the manning river.
During the migration times the bullies are relatively common. A good burley trail over a nice deep area with a good drop off will probably show some bull sharks. Migratory Bull sharks do go up rivers but not to drop their pups. They do this so they can have 0 outside competition and will literally swim up rivers as far as the can go without any affect from freshwater. Im not particularly familiar with the Cooks river myself but if there are no obstructions that would stop bull sharks from pushing up the river then you have a great chance. If there is a barrier I would actually fish on the ocean side right near that barrier because it will act like a aggregating area where the moving bull sharks will stop and turn around.
I hope you find this information I have gathered after a lot of research, helpful. Just be ready because they are really big, a 3.5 meterey does not sound that long but they are muscular and built like a tank.