If 1 bar is indeed about 30 ft, I doubt there are many header tank systems
that get near this for a first floor bathroom.

Indeed. I can't think that more than 1% of gravity based systems would
satisfy me for a shower, although oddly, my mother's downstairs shower would
have been close had I installed it before the mains pressure cylinder went
in (thin 4 storey Victorian house). That would have had about 9m head, which
would probably have sufficed. Either a pump or mains pressure is required
normally.

Christian.