Weekdays there's a staff bus ( the BA1) that you
might be allowed to use if you show your paperwork, but even if you get on its goes right around the airport via the A4 and it can take half an hour at least to make the journey.
A better bet might be the 423 bus to Hatton Cross, Cranebank is then about a 10 min walk (max).
http://http://www.londonbusroutes.net/times/423.htm
However personally I reckon it's quicker and less hassle to use the Underground: T5 has it's own station, so just take the tube to Hatton Cross and then the same walk as above.
Failing all that there are a few local cab companies (e.g LHR Cabs) who would probably do a one way run for, at a guess, around £15.