Bostock was a son of Dr. John Bostock, Sr. He spent some time at New College at Hackney where he attended Joseph Priestley's lectures on chemistry and natural philosophy, before graduating in Medicine at the University of Edinburgh and practising medicine in Liverpool. He moved to London in 1817 where he concentrated on general science. In 1819, Bostock was first to accurately describe hay fever as a disease that affected the upper respiratory tract.
Bostock was one of the first chemical pathologists. He was the first to realise the relationship between the diminution of urea in urine as it rose in the blood, while the albumin in the blood fell as that in the urine increased. His most noted book, System of Physiology, appeared in 1824. His only geological work was On the Purification of Thames Water which appeared in 1826.