Transfer from London Heathrow to Bath

We were meeting up with our Rick Steves Best of England tour in Bath last spring (2018).
We took the National Express bus from Heathrow to Bath. Comfy seats, WiFi onboard, a pleasant and scenic ride.
Just walk up to the window in the Heathrow bus station, buy your ticket, wait/sit outside on the benches for the bus to pull into the stalls.

Thanks for your very prompt reply! It sounds like you had not reserved your seat or purchased your ticket before leaving the US. Is this correct? Were you able to sit together and get on the next available bus or might we potentially have to wait for hours for the next open seat?

We just walked up and bought tickets at the window.
Did not reserve or purchase ahead of time.

No problem getting a seat.
There were two of us, and the bus had approximately 4 more passengers.
Practically empty.

When are you going. We are planning on the train from paddington station On sept 14 to catch some of the Jane Austin festival before the tour group.

The direct bus/coach that Rebecca took sounds good.

For info, additional options from Heathrow:
RailAir bus/coach direct from Heathrow Central bus station to Reading railway station, then board a train to Bath Spa.

Or : Heathrow Express to London Paddington ( Advance all-day cheaper tickets can be bought online) then train Paddington to Bath Spa, this is the same line/train that stops at Reading, but Paddington is at the start of the journey, You are doing a double-back to London this way though.

https://www.heathrow.com/transport-and-directions/buses-and-coaches/rail_air-bus-links

We took the National Express bus from Heathrow to Bath last September and it was a slam dunk. Walk to the window, purchase tickets and wait for bus to arrive. Couldn’t be simpler. Very easy, comfortable and you can snooze on the bus.

An alternative is to fly into Bristol instead of Heathrow. If you are coming from the USA, you can make a connection in Dublin for Bristol. Bath is a short bus or train ride away.

You asked for the best option. Nothing wrong with the bus option, but in my opinion a private car service is the best option. We've used car services in different locations and our experience has been that using a service based in the destination city works well as they always seem to know "the best way home". We used one based in Bath to go to the Bristol airport but we would not hesitate to use them from Heathrow to Bath. The web site is chauffertravel.co.uk and the email address is [email protected]. We sent an email detailing our needs and had a reply within 24 hours. Not sure about the price since we didn't actually take that trip, but by the time you total up bus / train fares, the hassle factor, time involved, all while being jet lagged, it's a small luxury we feel is well worth the price.

After a long flight we used Celtic Horizon private transportation directly to Bath. Neil was great and very informative.