Bainham, who hailed from Westbury-on-Severn, Gloucestershire, was the youngest son of Sir Alexander Bainham and his wife, Elizabeth Langley (née Tracy), became a lawyer after entering London's Inns of Court. Bainham's maternal uncle had been a reformer and perhaps he influenced his nephew. According to John Foxe, Bainham was "an earnest reader of Scriptures, [and] a great maintainer of the godly".
Bainham went on to marry the widow of reformer Simon Fish, a man who had been charged with heresy and was awaiting trial when he died of plague in 1531. Fish was the author of the religious pamphlet The Supplication of Beggars, which Anne Boleyn was said to have shared with Henry VIII. The pamphlet was an attack on the Catholic Church. Fish claimed that the Catholic clergy usurped the power of the state and stated that they were treasonous and corrupt. Fish also attacked the sale of indulgences and the doctrine of purgatory. Bainham came to the notice of Sir Thomas More, Henry VIII's Lord Chancellor, due to his links with Fish, and More had him brought to him for questioning. Bainham stood firm in his evangelical faith so More ordered his imprisonment in the Tower of London, where he was also allegedly tortured.