William Bock (the name Rose was added later) was born in Hobart, Van Diemen's Land (Tasmania), on 5 January 1847, the son of Thomas Bock and Mary Ann Cameron, née Spencer, both of whom had been transported to Van Diemen's Land and subsequently pardoned. He was introduced to his craft by his family; his father was a notable engraver, lithographer and daguerrotypist, important for his paintings of Tasmanian Aborigines. William served an apprenticeship of 2½ years in Hobart with his half-brother, Alfred Bock.
Failing to find employment on the Australian mainland, William Bock sailed to New Zealand on the Gothenburg in 1868. He arrived on 6 May in Wellington, where he was based for the rest of his life. After working with James Hughes for over five years, he went back to Tasmania and married his long-standing fiancée, Rebecca Finlay, in Hobart on 14 February 1874. On his return he managed the lithography and printing department of Lyon and Blair. In 1878 he rejoined Hughes for a year. He next set up his own business as an engraver and lithographic printer, first independently, then in partnership with Henry Elliott (briefly) and later with Alfred Cousins (1883–89). In the 1870s he was responsible for the design and preparation of the dies for the first fiscal and postage stamps to be produced wholly within the colony. In 1885 he designed the medals and certificates for the New Zealand Industrial Exhibition, at which Bock and Cousins were awarded a silver medal for engraving. They also gained first prize in engraving and die-sinking, and in lithographic and ornamental printing.
In the later 1880s William Bock personally supervised the first full book in chromolithography to be printed entirely in New Zealand. The magnificent Art album of New Zealand flora produced by Edward and Sarah Featon was published with 40 colour plates by Bock and Cousins in 1889. However, the strain imposed by the production proved excessive; further planned volumes did not appear, and the partnership with Cousins was dissolved that same year. Bock carried on business alone, initially as Bock and Company, and gradually recovered from debts of over £800.
Bock's artistic flair was demonstrated in his work as medallist, stamp designer and engraver, and illuminator. His medals included several marking the 1901 royal visit to New Zealand and the 1913 HMS New Zealand medal. He contributed four values to the 1898 pictorial stamp issue, widely acclaimed as one of the contemporary world's most attractive. In 1906 he engraved the New Zealand International Exhibition set, the first locally produced large commemorative issue. Bock was the most important and innovative contributor to the development of New Zealand stamp production from 1875 to 1931. His work as illuminator included two jubilee addresses to Queen Victoria and other addresses to Pope Pius IX and to visiting members of the royal family: 'nobody of any note visiting New Zealand left without taking away some memento of Mr Bock's skill'.
A robust, cheerful and optimistic man of medium height, William Bock had a wide range of interests including singing, drama, cricket, the Anglican church and the artillery volunteers. He was vice president of the Master Printers' Association. In later years Bock began a partnership with his son William and at his death was supervising the apprenticeship of his grandson F. R. Bock, who was to continue the Bock engraving tradition in Wellington. Rebecca Bock died on 19 March 1915 and William died on 3 August 1932. They were survived by two sons and two daughters.