The way aquaponics works is actually simple if you do it right.

1. Create a system that has fish that live off various algaes.
2. Provide the fish with light so that algae can grow in the tank.
3. The fish eat the algae along with food you provide for them if needed and produce waste.
4. The water goes into a mixing station where it is mixed well with the water and then from there it goes through a filter to filter out large particles and then into the bubble bucket.

You will need aeration for the fish tank and the bubble bucket. The more oxygenated your bubble bucket is the better your roots will do. It may also be a good idea to set up a uv sterilizer in the mixing station to avoid any algae trespassing into the bubble bucket.

If you do it right you can grow a plant without spending that much money on nutes though the cost of upkeep of the fish and the energy for the light may offset that cost.