William Bundey (born 1826) was Mayor of Adelaide, South Australia from 1883 to 1886 and a long serving member of the South Australian Legislative Assembly.
Bundey was born in Beaulieu, Hampshire. On 12 June 1848 he married Elizabeth Brandis at St James Church, Paddington, London.
The family emigrated to South Australia, arriving in December 1848.
He is buried in Walkerville cemetery, Adelaide.