Bath has a number of Anglican parish-based graveyards, some non-conformist burial grounds and, from the mid-1800s, ward-based cemeteries that catered for both Anglicans and nonconformists.  Although hotly debated in 1859, it was not until 1937 that Bath had a single municipal cemetery at Haycombe and, even then, the ‘closed’ cemeteries continued with burials.
To help family historians locate the place of burial, a Bath Burial Index has been produced.  In September 2016 this went online at the Bath Record Office website . It covers over 45 of Bath’s cemeteries and has over 240,000 burial entries, over 30,000 images of memorials, maps and documentation of inscriptions for some cemeteries. The descriptions of the cemeteries indicate where documentation can be found.
It includes municipal cemeteries such as Lyncombe & Widcombe and St James (Lower Bristol Road), Locksbrook (Walcot, St Saviour’s and Weston sections), Twerton (Bellotts Road), Smallcombe Vale and Haycombe which are not covered by the National Burial Index. 
It would seem that Bath is the only English city which has burial records for municipal and church-based graveyards in one place, online and freely-accessible.

Thanks to Phil Bendall for compiling and providing the above information