The eldest son of the Reverend Thomas Bonney, master of the grammar school at Rugeley in Staffordshire, Bonney was born in Rugeley. Educated at Uppingham and St John's College, Cambridge, he graduated as 12th wrangler in 1856, and was ordained in the following year.
From 1856 to 1861 he was mathematical master at Westminster School, and he pursued geology only as a recreational activity, mainly in Alpine regions. In 1868 he was appointed tutor at St John's College and lecturer in geology. His attention was specially directed to the study of the igneous and metamorphic rocks in Alpine regions and in various parts of England (eg: the Lizard in Cornwall, at Salcombe and in the Charnwood Forest), Wales and the Scottish Highlands.
In 1877 he was chosen professor of geology in University College London. He became secretary and later president of the Geological Society (1884-1886), secretary of the British Association (1881-1885), president of the Mineralogical Society and of the Alpine Club. In 1887, Bonney was appointed honorary canon of Manchester.
His purely scientific works are: