Richard Bullock Andrews was born in Epping, Essex, England the eldest child of Richard Bullock Andrews, an attorney, and his wife Emma Ann. From December 1839 Bullock worked in his father's solicitors business. On 15 August 1846 he married Elizabeth Holtaway, daughter of a solicitor.
Andrews emigrated to South Australia, arriving there 14 December 1852 aboard the steamship Sydney. In 1853 he was appointed a notary public, on 3 May 1853 he was admitted to practice in the Supreme Court of South Australia. He practised in the Local Court at Mount Barker, South Australia and then set up an office in Adelaide.
In June 1857 he was elected to the House of Assembly for Yatala and was attorney-general in the Torrens ministry from 1 to 30 September. He was again attorney-general in the Dutton and Ayers ministries in 1863, 1865, 1867 and 1868. He had been made a Queen's Counsel (Q.C.) in 1865 and in January 1870 resigned from parliament to become crown solicitor and public prosecutor. In March 1881 he was appointed a judge of the Supreme Court. He fell into ill-health, was obliged to take six months leave of absence at the end of 1883 and died at Hobart on 26 June 1884 leaving a widow and a daughter.
Andrews was an excellent public prosecutor and had the attributes of a good judge. His health however gave him few opportunities of showing this during the short time he was on the bench. In private life he was an amateur viticulturist, planting seventeen acres of vines; he made some good wines during the 1860s.