Transportation from London to Bath

You can take a direct bus from London Heathrow to Bath.

But as in a previous thread, it all depends on your arrival time.
https://community.ricksteves.com/travel-forum/england/waiting-for-godot-bath

You can access Heathrow Central Bus Station from any terminal. You may need to ride the tube between terminals. (Free), but you can get there without much difficulty. I did this trip in reverse a few weeks ago and the National Express bus worked well for me.

Whatever the paper work says the bus to Reading also leaves from Terminal 5, so if you land there you don't have to transfer to Terminals 2 and 3 for the Central Bus Station.
On Rail Strike Days the trains from Reading to Bath are hourly, rather than their usual half hourly, and last one at 8pm- much earlier than normal.
As you don't know what time you will actually arrive you can't book the train ahead. If the train is busy there is always a chance you may not get a seat, especially on a strike day when they are busy- not a big chance but you never know,
The direct bus to Bath only leaves from the Central Bus Station. Unlike the train you can book that bus ahead of time, get advantage of a good fare, and add on a £5 extra charge to be able to change your time if your flight is late arriving. And you know you have a seat.

There isn't a right answer. Pluses and minuses to both options. Many people prefer the coach to Bath for the convenience of no change. Others the train for the speed.