Joseph John Richard Bagshawe was born on the 1st July 1870 in Hampstead, into an affluent Catholic family; his father was County Court Judge William Henry Gunning Bagshawe KC (1825–1901), himself cousin of the famous rower William Leonard Gill Bagshawe (1828-1854). Bagshawe also had an artistic lineage, being a grandson of the leading Victorian marine painter Clarkson Frederick Stanfield RA (1793–1867). He received a first-rate London education, before studying under Hubert Vos (1855–1935) at the Royal College of Art.
Bagshawe first visited North Yorkshire in 1896 on a family holiday to Whitby, where they stayed at no. 1 Mulgrave Place. The holiday would have a profound impact on young Joseph, both on his later decision to move to Whitby permanently, and because it was here that he would meet his future wife, Mildred Turnbull, the only daughter of prominent Whitby shipyard owner Thomas Turnbull. It would be another two years before the pair would meet again, but on the 15th September 1898, they became engaged to be married. 1901 seems to have been perhaps the busiest year for Joseph Bagshawe, for it was here that he became a founding member of the Staithes Art Club, serving as its first secretary, and a few months later, on the 3rd September, that his and Mildred's wedding took place at St Hilda's Church, Whitby. The two soon settled at the Old Rectory in Whitby.
The wedding was also a significant milestone in Joseph's artistic career, for his wedding present from his new father-in-law was a yacht. This allowed Bagshawe to continue his fascination with the sea that had begun with him taking trips out to sea with the Staithes fishermen. He was a keen and competent yachtsman, often leaving on trips that lasted as long as a fortnight, and this skill is evident in Bagshawe's paintings of ships and the sea, perhaps the most accurate and lifelike of any of the Staithes Group.
Joseph Bagshawe exhibited widely, at the Royal Academy, the Royal Society of British Artists (of which he was elected a member in 1904), the Royal Institute of Painters in Oils, Manchester Art Gallery, the Walker Gallery, Liverpool, and of course the Staithes Art Club. He died tragically on the 1st November 1909, at the young age of 39, from complications of diabetes. He is succeeded by his great-granddaughters, the author and former Member of Parliament, Louise Mensch and the author and journalist, Tilly Bagshawe.