The dishwasher tablets are the best thing for this type of bath.
Boiling water and a few dishwasher tablets in a bucket, wait till they disolve and then put into bath.
Turn on the bath and the solution will run through the system.
EVERYTHING that is in the system will come out, hair, grit grime and probably fecal matter (UGH!)
Horrible as that sounds all these things are probably in any whirlpool bath system.
Regards
Martin