He was the son of John Bagshaw of Rugby, Warwickshire.
He moved to Harwich in Essex and acquired land at nearby Dovercourt, where he developed plans with the help of W.H. Lindsey, a London architect, to build a new resort overlooking the sea. He started the project in 1845 by building a mansion, Cliff House, for himself and his family and actively promoted a railway link to Harwich. When a chalybeate spring was discovered in the grounds of Cliff House, Bagshaw extended the property to incorporate a spa, library, pump room, and conservatory. He next developed Orwell Terrace where his son Robert John Bagshaw, also an MP for Harwich, moved into Banksea House in 1857. However the developments, which included Marine Parade and the Cliff Estate, caused him financial difficulties and he was declared bankrupt in 1859.
He was elected at the 1835 general election as Member of Parliament (MP) for Sudbury, having unsuccessfully contested the seat at a by-election in July 1834. At the 1837 general election, he did not stand again in Sudbury, but contested Kidderminster unsuccessfully. At the 1841 general election he stood instead in Harwich, but was not elected. He won the seat in 1847, but was defeated in 1852. However, the election of his Conservative Party successor was voided on petition, and Bagshaw won the resulting by-election on 21 June 1853. After being re-elected in 1857, he resigned his seat in the House of Commons on 9 March 1859, through appointment as Steward of the Chiltern Hundreds.
He died in Norwood in 1861 after the contents of his house and spa had been sold and his estate broken up. Cliff House was demolished in 1909 and the Spa in 1920. He had married twice and had a son and 3 daughters. His son John Robert continued the development of Dovercourt and also became MP for Harwich.
- Leigh Rayment's Historical List of MPs – Constituencies beginning with "S" (part 6)
- "Harwich and Dovercourt". Retrieved 14 May 2018.
- Craig, F. W. S. (1989) . British parliamentary election results 1832–1885 (2nd ed.). Chichester: Parliamentary Research Services. p. 294. ISBN 0-900178-26-4.
- Craig, op. cit., page 165
- Craig, op. cit., pages 144–145
- Department of Information Services (9 June 2009). "Appointments to the Chiltern Hundreds and Manor of Northstead Stewardships since 1850" (PDF). House of Commons Library. Archived from the original (PDF) on 6 February 2011. Retrieved 30 November 2009.