To unclog a bathtub drain the right way, you'll need to take the drain plate off. That's the little round plate that has the lever on it for opening and closing the pop-up drain stopper. It takes a little effort, but it's not too hard to remove and behind that plate, you have access to a straight drain pipe you can send the drain snake down. Check out the video above from This Old House for instructions.
I just had my pipe under the sink unclogged and new pipes put in $600.00, then they flushed out the pipe from under the sink to the outside pipe $700.00, Total of $1.600.00, I thought that the price was high, I got the plumber from Home Advisors, not sure they had to do all they did but they said I needed the work done. The same evening hike using the dishwasher I had a leak in one of the pipes they put in, they came back the next day to fix it. Don't know if I will use them again.. They were K&D kitchens.
Plumbers in Australia have licensing requirements that differ from state to state but it is generally accepted a 4-year apprenticeship with a further minimum experience of 2 years (6 years total) and a further curricular requirement as a benchmark for licensing. Licensed plumbers are also expected to maintain minimum relevant training requirements to maintain their plumbing license