In message .com,
" writes

What is the best way by public transport?

There is a direct Express Bus service that runs roughly half-hourly,
taking 90 minutes (although allow extra time just in case). Details at
http://www.nationalexpress.com/home/hp.cfm

Travelling by train is more expensive and is unlikely to be much
quicker. The Stansted Express (every 15 minutes) takes 45 minutes into
Central London, you would then need to take the tube to Paddington,
followed by the (expensive) Heathrow Express to Heathrow (total time
about 100 minutes).

A cheaper rail+tube route is Stansted Express to Tottenham Hale, then
Victoria Line to Green Park, then Piccadilly Line to Heathrow - about 2
hours in all, and the interchange at Green Park is inconvenient if you
have much luggage.
--
Paul Terry