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Bath was run by an elected council- the Corporation.

If I may, I shall quote the following from Trevor Fawcett's very informative bookBath Administer'd(2001), on the duties and privileges enjoyed by Corporation members( because it sums up the position beautifully and far better than I could manage):

Routine day-to-day or emergency business was handled by an executive team of Mayor and magistrates, advised and aided as required by the other chief officers and the Town Clerk.

The growing complexity of municipal affairs led to sum devolution of responsibility( e.g. for city highways from 1766 to the Bath Commissioners) and the appointment of paid deputies or bureaucrats( notably the Chamberlain's office0 as a way of shoring up what ws now an archaic structure.

The City Council took the longer-term decisions and issued by-laws, yet here again much of the detailed investigation and drafting of proposals was devolved, this time to committees. What with regular calls to serve office( with penalties for unjustified refusal) Council meetings , committees , judicial duties, attendance at civic functions and extra mural business of all sorts, the Corporation elite lived busy lives.

But of course there were compensations- the sense of status and power, the opportunities for social climbing and hobnobbing with the great and good( even with royalty if they were lucky), the chance to steer municipal policies for personal advantage and- not to be cynically dismissed- the altruistic satisfactions of public service and civic virtue.

To be on the Council was to be in the know, to be part of the club, to share in the dispensing of patronage, and to enjoy privileges and the paraphernalia of membership-civic processions and entertainments, a special pew in the Abbey and a place in the gallery of portraits hanging in the Guildhall

With regard to the Pump Room, strictly the Corporation was responsible only for the hot springs. However the Corporation built and staffed the Pump Room and the Hot Baths.

Does that help?