Is there any particular reason that you can't use the Underground? It would be simpler.
By Underground:
Take a westbound train on either the Circle Line or the District Line for 2 stops, to South Kensington. Transfer to a westbound Piccadilly Line train. Some trains serve terminals 1. 2, 3 and 4. Others serve terminals 1, 2,3 and 5. The total journey time is approximately 1 hour. (If travelling by train to London, buy a ticket to 'Zone 6' which will include your Underground travel to the airport.)
By Underground and National Rail:
Take a westbound Circle Line train for 7 stops to Paddington. Then take the Heathrow Express to the airport. Again the total journey time is about 1 hour but this route is useful if you're travelling by train into London as you can book a through ticket to Heathrow.
By bus:
Walk to Victoria Coach Station. (It's fairly well-signposted but it's quite a hike, especially with luggage. Allow 15 to 20 minutes). Then take service 033, 403, 501 or 504 to Heathrow Central Bus Station. Buses leave on the hour and half hour (but with some gaps in the schedule, so you might have to wait for nearly an hour if you've just missed a bus) and take about 45 minutes. (But remember to allow further time, of perhaps 20 minutes, to get to your terminal from there).
To check details, start here;
http://journeyplanner...er/XSLT_TRIP_REQUEST2
Chris