get to Bristol City Centre from London Stansted Airport?

Stansted Express train to Liverpool Street station in London … tube Circle line from Liverpool Street station to Paddington station … train from Paddington to Bristol
have a look at the tube map
http://www.tfl.gov.uk/assets/downloads/standard-tube-map.pdf
don’t take the Hammersmith & City line from Liverpool Street to Paddington as it will take you to the “wrong” end of the train station
for train times and bookings use http://www.thetrainline.com … you might be able to book an all-inclusive end-to-end ticket including the tube