Here is a bus route map serves LHR:

http://www.milesfaster.co.uk/informa...w-freeflow.pdf

The easiest way from T4 to Marriott is to take 555 bus and get off at Harlington Corner. (I think you need to cross street and look for a McDonald, Marriott is right next to it).

Or you can use Heathrow Connect from T4 to go to Terminal 1/2/3 where the central bus station is. From there, you have several choices of bus line.