Bliss was born in the Cotswolds village of Bisley in Gloucestershire and studied at Pembroke College, Oxford.
Rector of St Ebb's church in Oxford, he succeeded Edmond Halley as professor of geometry at Oxford University in 1742 and was elected a Fellow of the Royal Society the same year. He succeeded James Bradley to become the fourth Astronomer Royal in 1762.
He died in Oxford but was buried close to Halley in St Margaret's churchyard in Lee in south-east London.