Bashforth studied at Cambridge University, where he was Second Wrangler (second highest scoring candidate) in the 1843 Tripos Test. Between 1864 and 1880 he undertook some systematic ballistics experiments that studied the resistance of air. He also studied liquid drops and surface tension.
Later he was a fellow at Saint John"s College at Cambridge University. From 1857 until 1892, he was the school rector at Minting in Lincolnshire. He invented a ballistic chronograph.
At times, he was also a professor of mathematics at the Royal Military Academy, Woolwich.
The Adams–Bashforth method (a numerical integration method) is named after John Couch Adams (who was the 1847 Senior Wrangler) and Bashforth. They used the method to study drop formation in 1883.
