Here is what the Courtyard website says:

"Situated near the MTR subway – HKU station (exit B1) of West Island Line with approximate 6 mins on foot."

AND:

"public transit for Hong Kong International Airport – A12 bus in front of the hotel’s main entrance."

AND:

"Complimentary hotel shuttle bus service from and to nearby landmarks and major financial districts."

The hotel website doesn't mention anything about the AE train, although from looking at the airport website, it seems that there is a free shuttle from Central to many hotels.

"Free shuttle bus service is available, taking passengers from Kowloon or Hong Kong stations to most major hotels and transport interchanges."