Train or bus from London Heathrow to Bath

It depends on the day of the week.
The bus is infrequent, so on some days of the week you could have a wait of up to three hours.
As well as National Express Flixbus now also run to Bath, but also only every few hours.

Compare that to every half hour by train. The drawback of the train is that you are getting toward peak hour on a weekday, when the trains are very busy, but also at their most expensive.

My own feeling is that I would play it by ear, aim for the 4.40pm bus on a Monday to Thursday (Friday to Sunday it is at 3.10 or 6.20 pm). If I'd missed that the rail/Air bus to Reading Station then hang around for the first cheap and less crowded train at just after 7pm. (get a drink or dinner close to the station in the meantime).

it sounds to me that you are planning on leaving from central London as you will have been in London for a few days before going to Bath? Yes?

If so, it would be very handy to know where you are staying to give you the best route either to the coach (not a bus) or the train.

or is the 3:00 when you flight lands and your departure to Bath a completely different time?

sorry for the questions but I'm confused and want to help

The plane lands at Heathrow at 3:00P.M, and our tour starts a few days after that. We won't be exploring London before the start of the tour. Just want to get to Bath from Heathrow, London within the same day that the plane lands.

There are probably more direct ways (and cheaper ways), but I'd take the Heathrow Express to Paddington and then buy a ticket there to Bath. This provides you the greatest flexibility and will not take all that much longer than other options. Heathrow Express tickets can be purchased at Heathrow and there are 4 trains every hour. From there, trains leave Paddington for Bath every 30 minutes or so and take about 1 hour 20 minutes. If you can figure out the direct bus schedule you'll save time and money over this option, but I prefer the trains over the bus travel generally speaking.

Seconding the Heathrow Express to Paddington - Paddington to Bath Spa via train route based on my recent trip. Very flexible and easy.

Using the Heathrow Express in early May you are going to miss the cheaper Advance tickets. Taking an Elizabeth line train to Paddington instead will be a bit slower but be cheaper if that’s important.

Just go to www.nationalrail.co.uk and look up the route there. No need to second guess.

Fastest is Elisabeth line to Hayes, change there for Reading, and then board a train to Bath there. Runs every half hour, and will be cheaper than going all the way to London.