...the Burgermasters said NO.
Can you give links to the Network Rail proposal you refer to, and the response to them? I'm not sure who these burgermasters you refer to are: the council? The Bath Preservation Trust certainly appear to have struck a pragmatic balance between the requirements of electrification and the need (for it is a need) to protect Bath.
I can't provide a link but I attended one of the drop in sessions at the Guildhall in Bath in 2015 and the subject of the OHL▸ (Over-Head Line) was definitely raised. Looking at the artists impression of a service passing through Sydney Gardens the OHL support depicted is not of a typical GWML▸ (Great Western Main Line) OHL structure. There might even have been display boards depicting the designs forwarded for consideration but thats all academic now as it seems GWML electrification ceases at Wooton Bassett for the foreseeable future.
The Bath Preservation Trust are probably consulted on matters concerning changing the face of Bath like the likes of The Merchant Venturers and Bristol Civic Societies are similarly used in Bristol.