I would second the train to Feltham from Waterloo and then the 285 bus to Heathrow. Combined rail and bus tickets can be purchased at Waterloo station.
see:
http://www.baa.com/doc/6d33169bbd811...eec3_main.html
The total cost is around 5.40pounds (4.40 for the train and 1pound for the bus)
(The train operates every 10 to 20 mins and takes about 25 of 30 mins. to reach Feltham. The bus operates every 10 mins. from Feltham to Heathrow)