From Paddington you have two options really......go via tube which takes forever or use the heathrow express.
Crew can get this for £130 pound a month (used to be £110)
You would then get the 111 or the 105 from the Central Bus Station at heathrow to the Compass Centre or one of the BA staff shuttles there.
The only problem is that the Heathrow Express is not a 24/7 and the first 5.10 morning departure does not get you in on time for the first report.
You could also use the Night Bus service, but its not fun or clean when you have to share it with tramps and late night clubbers wreaking of alcohol and kebabs! lol