How long will it take to walk from terminal 2 to the buses to Bath.
The one time we took a bus to Bath it was from the National bus terminal near Victoria station. Are you sure there is bus service from Heathrow?
We took the bus from Bath to Heathrow, so it must go the other way as well. You can look at maps of Heathrow and judge the distance. As I recall there were multiple elevator rides involved.
Depends which way you want to go and how able bodied you are. I think the signs direct you through the underground passages to Heathrow Central Bus Station, but this requires a change of level at either end. It is shorter to do it on the surface, but that means being outside in any bad weather, plus you have to cross roads. Possibly best to stay with the signed route being unfamiliar.
We have often arrived at Term. 2 and walked to the bus station to take a bus to Winchester. There are very visible signs, so that makes it easy. There is a curvy ramp to go down a level so you have to be able to handle your luggage cart, if you have one, or it will run away on you, but it was never a problem for me. When you reach the Tube level, there is an elevator down to the bus station level.