Bryden was born in Edinburgh and went to Edinburgh high school before going to the University of Edinburgh from which he received an MD in 1855. He received a gold medal for a thesis on sugar in the liver, as glycogen had then been discovered by Claude Bernard. He joined the East India Company Service as an assistant surgeon and reached Calcutta in December 1856. He escaped the 1857 rebellion from Mundlaisir and returned to Calcutta. He was posted in Lucknow and later in northern Bengal. He then became a statistical officer under the sanitary commissioner J.M. Cuningham working on cholera epidemiology. He believed that cholera was spread by an airborne agent and became an epidemic under specific conditions which he believed he could predict based on the weather. After 1870, the cholera germ theory became more dominant and led to his airborne theory being entirely dismissed later.