The free bus you will have caught was a No423, sadly thats the only bus that goes past the Premier inn gates and doesn't go to heathrow central bus station (for terms 1 & 3). However the A4 (still called Bath Road) which is at other side of your hotel and joins at end of road (colnbrook bypass) has buses 75 & 76 plus possibly others that you can catch(its in the free flow area.
Not sure where the nearest stop is though so maybe a short walk.
To be honest i go for other hotels along Bath road (A4) between where you are and Harlington corner as you can get everywhere (all terms) from them and all in the freeflow area.
From top of my head these are the hotels i'd go for depending on best deal - Arora, Holiday Inn, Park Inn, Renaisance, Sheraton Skyline, Radisson Edwardian.
http://micks-travels.blogspot.co.uk/
Just select Heathrow or Handy Tips from the pick lists in the r/h column.
Dont know if you want Hotel and Parking but can get some excellent deals, when i go to Slovenia for a week in May got 4 star hotel (park inn) & parking for only £62, and £71 when i go to America (two weeks parking & same hotel) in november.
Hope it helps
Mick