Britrail pass

The airport express train is only covered if it falls on one of the days covered by the Pass. So your return to Heathrow after the four days would not be included.

Price of thickets for the Heathrow Express depend on when you buy them and when you travel. Full fare is £22-25 depending on Peak or off-Peak travel. But if you buy well in advance, they can be as low as £5.50 ( weekend or bank holiday travel, bought 90+ days in advance) (£12.50 for weekdays). If your daughter is under 16 she rides with you for free on the Heathrow Express.

[Edited - 2nd post is below.] The Heathrow Express is covered the same as any other train under the National Rail umbrella. On your travel day from Heathrow to Bath, you can have the pass activated at the airport train station, hop the Heathrow Express to Paddington station, and connect there for trains to Bath.

I don't know when you're traveling, I realize that last-minute ticket prices in England can be very high, and I know nothing about ticket prices for children. Still, I wonder if you would really save money with the pass. Have you checked individual ticket prices on the National Rail website for your travel dates, or as close as you can get if your trip is far in the future? It's not like you're traveling back and forth to distant places like Edinburgh.

I quite doubt that you would save any money on that pass.

Nationally, a child under 16 travelling with you is half price, and very inexpensive fares are available if you know where to look and a few of the tricks of the trade.

When is your trip?

So if I buy individual tickets online ahead of time my 13 year old daughter is half price? We are going in late June.

Not only is she only half fare, you can do even better than that.

If you will pay more than £100 total (in a year) on train tickets together you can buy a £30 Family and Friends Railcard. As long as you travel together, and as long as she is under 16 when you buy that Railcard you can get a 30% discount on almost all tickets for yourself and 60% off her half price fare (minimum fare for her is £1.00).

There is a restriction that if the train trip starts and finishes within the old Network SouthEast area - now called London and South East - it is only valid after the morning peak hours.

None of your trips fall into that category so you could use it on all your journeys.

If you use the Advance (with a capital A) tickets and get them well ahead (and understand their non-refund status), and use your railcard we can keep the outgoings to a minimum.

I haven't worked out the fares but it easily done with the National Rail website or app. If I have time later I'll perhaps have a shot at it.

Actually, I mis-read Bath as "York" in the second half of your sentence. Since your range is smaller than I thought, you can do the trip with a BritRail London Plus pass, $189 for both of you for 4 travel days within a month. (This pass used to have separate vouchers that let you take the airport train at a later time, but that structure changed a couple of years ago.)

If you do end up buying tickets online or locally, a "Return" (roundtrip) ticket is often cheaper than two one-ways.

Heathrow Express is covered the same as any other train under the National Rail umbrella

With my purely pedantic hat on, sorry, for the benefit of other pedants and interested parties, and for the avoidance of confusion at a later date I wish to offer the following:-

National Rail is a construct of ATOC, the Association of Train Operating Companies, now replaced by the renamed Rail Delivery Group (sexy, eh?) for the benefit of passengers and to resemble the old British Rail, allowing the member companies to function together and represent them.

Heathrow Express is owned by Heathrow Airport and is not a Train Operating Company in the meaning of the Act, and is not a member of RDG and wasn't a member of ATOC, and didn't exist (nor did the route) in British Rail days.

However it is covered by the BritRail pass regardless. BritRail is another construct of the RDG purely for marketing internationally.

So, for our original poster, Joanna, and for many other readers it will make no difference, but it a good thing, IMHO, to be accurate.