Has water from the bath ever drained away correctly?
Does the bath waste pipe go into a 4" / 110mm vertical stack pipe?
Does the sink / basin on the same line drain away O.K ?
As LastPlumber has said, an air admittance valve or anti-syphon trap is unlikely to resolve the issue.
It's not designed to help water flow away or to vent a waste pipe, it's to prevent water that does flow away from siphoning the water out of another waste trap and allowing smells inside.
If the bath has drained correctly in the past, it's most likely you have a blockage or partial blockage somewhere.
If the bath has never drained correctly it's probably a bad pipe layout from the bath.
I wouldn't be surprised if it was a Drain clearing "expert" who said an AAV will fix it, it seems to be their solution when they can't find a blockage.
I've encountered them many many times offering that solution, when it's not needed.