drain is an easy fix - chuck out the metal grid , get a plastic one , lengthen the pipe to discharge below the grid ( above the standing water ) cut the grid to fit round the pipe (y)
then the bath trap is dry - you could verify that by a small stick dipstick - coffee stirrer - waterless trap Hep V O on the bath (it's anti vac/non return ) so the lashed up "vent" system is not working.