[1] His father owned a large farm, but as the second son he needed to seek a career outside farming, and so he studied medicine at Guy's Hospital Medical School), University of London, where he excelled, winning prizes and scholarships in Organic Chemistry and Materia Medica (scholarship and gold medal, 1864), Biology (scholarship, 1865), Geology and Palaeontology (first class honours, 1865), Medicine and Midwifery (first class honours, 1866), and Forensic Medicine (gold medal, 1866).

[2] In autumn 1872, Bushell and Thomas G. Grosvenor (1842–1886), a secretary at the British Legation, went on a journey beyond the Great Wall of China to Inner Mongolia, and visited the ruins of Shangdu (Samuel Taylor Coleridge's Xanadu), the fabled summer capital of the Yuan dynasty.

One of Bushell's many interests was numismatics, and he collected a number of coins issued by the Western Xia state with inscriptions in the Tangut script.

[7] Bushell was also able to confirm that the unknown script on the six-script inscription on the Cloud Platform at Juyongguan on the Great Wall of China was Tangut, and not Jurchen, as had been asserted by several previous authors, in particular Alexander Wylie in an 1870 paper entitled "An ancient Buddhist inscription at Keu-yung Kwan".

However he did publish a facsimile of a bronze 'fish tally' (yú fú 魚符) with a small character Khitan inscription that he had in his collection.

Although he did not actually publish anything relating to the 'Phags-pa script, during his time in China (probably on his 1872 trip to Inner Mongolia) he acquired the only extant manuscript copy of the early 14th century rhyming dictionary of Chinese written in the 'Phags-pa script (Menggu Ziyun 蒙古字韻), which was sold to the British Museum by his widow in April 1909.

[1][10] He also acquired a number of items for the British Museum, including a Tibetan skull cup in 1887 and collection of bronzes in 1898.

[2] After his death, his widow donated his collection of ceramics, antique pottery sherds, ancient Chinese knife and spade coins, hanging scrolls, and various other artefacts to the British Museum.