Originally Posted by
tdo-ca
... and an easy shuttle bus (hoppa) to take you there.
... which are slow, generally more infrequent than local buses (although less so for T4) and expensive. Honestly, nobody in the know takes them - the local bus service is much, much quicker and almost as convenient. I've noticed that even the hotels have stopped pushing the Hoppa service now, and are more likely to ask if you want a taxi.
I would personally also use the Hilton Garden Inn near Hatton Cross tube - it's no more than a three minute walk from the tube station.
Bus numbers 482 or 490 leave from stand A at the station, and will get you to T4 in five minutes the following morning for precisely nothing - Hatton Cross is within the Heathrow Free Ride Zone that the airport funds.