Try this bus sevice
Takes just over an hour and costs about £20
National Express Coaches // Coach & Bus Travel Throughout The UK
From the drop down select Heathrow T1-T3, that is where the bus station is.
If you are flying into T4 or T5 there is an underground train that will take you to T1 bus station. Don't attempt to get the bus direct from T4 or T5 they are few and far between and will make multiple stops
