<font face="Verdana, Arial, Helvetica, sans-serif" size="2">Originally posted by MileGuy:
Is the bus the fastest way to transfer coming in on AA, T3, connecting on BA going to AMS?
Can you walk? Is the train avail?</font>
There is a small obstacle between them (What's 10000m long and not a good idea to walk across?
).
Your best best is to take the Heathrow Express (HeX); it's non-stop, fast, free of charge between T3 & T4 - and nearer T3 arrivals than the tube (Which will require a ticket and a train change).
Regards,
Alex