National Rail from London to Bath

From Paddington:
Cheapest Advance: £14.50, although sometimes as low as £10 on promotion
Cheapest Walk-Up Fare: £33.10, valid after 10:10 but not valid between 15:30 and 19:01

There are ways of making it a bit cheaper splitting the ticket, or travelling on the infrequent route from Waterloo via Salisbury. I would only recommend the latter if doing a stop in Salisbury enroute.

If you are coming in at Heathrow you can take a bus direct to Bath, http://www.nationalexpress.com/coach/airport/heathrow-airport/index.html?utm_medium=businessdevelopment&utm_source=heathrowairport.com&utm_campaign=getting-into-london.

Walk-up fares in the UK can be really painfully expensive.

Do you have enough time to do an extra night in Bath? I love Bath and find there is so much to see there.

I've also done the route Marco mentions from Waterloo via Salisbury just for a change of scenery. I thought that route was prettier countryside BUT it was a lot slower and at that time (maybe 2013??) the train cars were much nicer on the Bath to Paddington route vs the route via Salisbury. That, of course, may have changed.

The Best of England does not go to Salisbury, Stonehenge or Old Sarum if those are of interest to you. Depending on how much time you have, it's easy to do an overnight in Salisbury (see the cathedral and Magna Carta that afternoon), the next AM take the local bus which runs a continuous loop out to Stonehenge and back thru Old Sarum for part of a day, then take a train on to Bath for the evening. It's under an hour from Salisbury to Bath.

Lots of good advice here already, so I won't repeat.

I'd like to add, consider doing as Bob recommended and take the bus from Heathrow to Bath. The reason for this would be, if you do not plan on doing any sightseeing in London before going to Bath.

If you want to spend time in London before going to Bath to begin your tour, then do take the train from London, as others have suggested.

However, if you want to get to Bath immediately upon landing at Heathrow, take the bus to Bath. Follow the signs in Heathrow to the Heathrow Bus Station. Lots of signs pointing the way. Approach the ticket window and buy your tickets to Bath. Not very expensive. Be sure to ask the bus number you will be traveling on.

Then you will go through the glass sliding doors, turn to the left, find a seat on one of the many benches. You will be facing the stalls where the buses pull in. Watch for your bus. There will not be an announcement made when your bus pulls in. The driver will get out of the bus, help passengers with luggage (put under the bus in a storage compartment) and then the bus will depart. The buses don't sit around for very long.

The bus will be slower than the train, but you will see a lot of scenery out of the window, and you will sit up high. The train is sometimes traveling down in a cut, low, so you see only bushes on either side of the train.

Rebecca is right. The bus is the way to go. Comfortable seats, luggage stored for you and you can have a nice little nap if you wish.

Thanks all for the advice. I should have given more details. We're arriving a couple days early to spend some time in London. So we'll be leaving from London, not Heathrow. We'll do the Paddington to Bath route. Will follow the British rail site and see if we can get any decent deals. Since our trip is in June, it'll be awhile before the online sales begins for those dates. I can't believe that British rail does not allow you to print your tickets online once you buy them. Instead, you have to pick them up at the station the day of. At least that is what I gathered from the website. May be there is alternative website where they allow it. They need to at least enter the late 20th century, much less 21st.

I did 6 weeks in the UK last year, about 90% by train. I did all my reservations online in advance from home and picked up all my tickets in Bath, my first stop. Most were limited to specific train departures, but some I could go anytime. Most were much cheaper than if I'd just walked up. For one ride, paying full price isn't a big deal, but for the number of rides I did and the distances I traveled, it meant a savings of hundreds of GBP.

If you search National Rail, you will see that there are actually multiple companies that operate the trains. There also are multiple fares depending on time of travel, if you have a railcard, etc. Do some dummy searches to see how it works and how much you might save.

And although all the train companies have lots of ticket choices and you can pay for the tickets online from home in advance, only one train company had the option to print the ticket at home.

Although regular pricing is the same, the individual operators do sometimes have promotions that are only available through their sales, so it is worth checking out GWR at the appropriate time.

New trains are being introduced onto this route which will become increasingly the norm through 2018.

I can't believe that British rail does not allow you to print your tickets online once you buy them. Instead, you have to pick them up at the station the day of.

Some train companies allow you to print tickets at home, but the one that runs the trains between London and Bath (GWR) does not. It is an issue of whether the ticket inspectors have been provided with the equipment to check tickets against the online database. Tickets are valid on more than one train, and they need to check that you haven't printed multiple copies and someone else has already used the ticket on a previous train, or someone at the other end of the train is not using the same ticket.

Picking up tickets at the station is easy, this is what most people do. You get a code number when you buy online, you have to put this humber and the card you used to buy the ticket into any ticket machine, and it prints your tickets.
Be sure to bring the same card that you used to buy the ticket, even if it is now out-of-date.
If you are passing the station you can pick up your tickets earlier, it does not have to be on the day.

You can also pick up your tickets at a different station than the one you are departing from, but you always need the code Nd the credit card you used for purchase.