The next entry for Bath in the British County Catalogue is for a handstamp 31 x 9 mm, known between 1760 and 1761. Unfortunately I don't have any examples that I can definitely fit in this date range - what I do have is firstly a free front franked by Charles Whitworth with a Bath straight-line handstamp that I measure at 30 x 8 mm.
Charles Whitworth was the MP for Minehead from 1747-1761 and then again from 1768-1774. This front must have come from one of the period when he was an MP and had the franking privilege, so could have come from 1760-1761.
Secondly I have an undated entire that was written to an MP, Sir William Codrington, with a London "FREE" mark on it that was in use from May 1764 to May 1766. The Bath handstamp matches the one above (see below).
The contents are the accounts for Barbuda for 1761-1763, including £60 for 3 slaves in 1761.
How to tell if two handstamps match ? What I have done to be confident that these handstamps match is to scan them both, and then use the computer to lie one on top of the other - by moving them about relative to each other one can determine if there is a reasonable match or not.