Bonham became deputy to the Governor of the Straits Settlements, Kenneth Murchison, in 1833. However, as Murchison was away from Southeast Asia for much of his governorship, Bonham was in effect responsible for the administration of the Straits Settlements. He took over from Murchison as Governor on 18 November 1836, a post he held until January 1843. He first governed from Penang, but later made Singapore the permanent residence of the Governor. During his governorship, Singapore grew in commercial importance as well as strategic significance as it supplied provisions for warships on their way to the Opium War in China. He was involved in the partial abolition of bond slavery, and provided a ship to combat piracy in the region. In an attempt to reduce the cost of administration, he reduced the number of senior officials from 19 to 8.