Bath traps are shallower than sink traps and clog faster because of the volume of hair passing through them. A weekly enzymatic treatment keeps the build-up down without damaging pipework.
Do not use caustic drain cleaner on old lead or copper waste pipes common in period properties — it corrodes them and creates a much more expensive problem.
Standing water that will not move at all, in more than one fixture, is a drain issue rather than a fixture issue.