London Train stations

Take the Elizabeth Line from Heathrow to Paddington Station.

GWR Trains from Paddington to Bath Spa take about an hour and a half.

https://www.gwr.com/stations-and-destinations/popular-routes/london-to-bath#

The London station would be Paddington, from which you can get to via the Elizabeth line, or the more expensive Heathrow Express, in about the same time.

The problem is, you will be going the opposite way, then need to backtrack to get to Bath, but it can be as fast. The other options are a bus directly to Bath, or a bus to Reading, then train to Bath. Others may have a preference or some recent experience.

We took the National Express Bus from Heathrow to Bath. A lot easier than taking a bus to Reading to catch train to Bath. Or going back to London to just turn around and take train to Bath. We do have some on here that live in England that will probably chime in on the best route.

Don't backtrack into London.

Take the bus to Reading and then the train to Bath. (It's the same train that you would have gotten at Paddington.)

or

Or you can take the Elizabeth line to Hayes & Harlington then transfer to another Elizabeth Line train to Reading.

or

You could take a National Express coach from Heathrow to Bath.

I've never done it, but taking the National Express bus straight from Heathrow to Bath sounds way easier than anything else.

I've done it twice, and taking the National Express coach (bus) straight from Heathrow to Bath is much easier than anything else.

The coach pulls in right beside the train station in Bath, so you end up exactly where you would have, had you taken the train.

Various Bath city buses are pulled into the stalls at the bus and coach station (it serves both).

Or you can easily walk to the downtown area; it's just a few blocks.

Thank you!! Do you know how price & travel time compare for the bus compared to the train?

Travel time is !little different. Bus just over 2 hours, train just on 2 hours if the connections work out. So 15 minutes or so difference.
Cost is hard to be exact due to dynamic pricing by both modes, but on an average day bus is about half the price of the train.
Frequency- bus is every 2 to 3 hours. Train is every 30 minutes.

So everyone works out their own cost versus frequency suitability. A very personal decision.