Bough was born in Carlisle, receiving his early training from Matthew Ellis Nutter and spending a short period in London circa 1839 studying under Thomas Allom. He then returned to Carlisle, remaining for 3 years before departing for Manchester in 1843 to take up a position as assistant scene painter at the Theatre Royal. Towards the end of 1848 he took up a similar position at Glasgow's Princess Theatre. After 1849 he became a full-time landscape painter following the success of Baggage Waggons – Carlisle in the Distance at the West of Scotland Academy. In 1855 he took up residence in Edinburgh and remained in Scotland for most of the rest of his life.