THe following buses, from stands 18, 19 and 20 (which are all together) all stop outside the LHR Marriott. You shouldn't wait more than a few minutes.

105,111,140,285,555,556,557

You'll pass the Renaissance on your right, then a McDonald's on the left, and it's the bus stop after that.

To return to the airport from the Marriott, head left out of the hotel, cross the road at the junction (about 100 yards) to the bus stop, and the same list of buses will return you to the LHR central bus station. I think the only bus that doesn't go the airport from here is the 222, so avoid that one