Gatwick to Bath

Should be possible with one change in Reading unless something has changed.

You can take the train to Reading and transfer to a train to Bath. Look up options on National Rail.
A bus will take twice as long and cost 1/2 as much. You can find that information on National Express.

You could take the Thameslink train to Farringdon from where there is step free access via the Elizabeth Line to Paddington for a train to Bath. Or go via Reading as said.

The Coach is unusual in that it is the same price (£33) whether you book on the day, or months in advance, changing at Heathrow.

The train via Farringdon has advance fares of about £45, half hourly.

The train via Reading is hourly at xx.29, and has a £73 walk up fare. But if you buy in advance as 2 tickets Gatwick to Reading and Reading to Bath you can bring this down to £38.

I'm not sure whether there is a clear "best option". Given the vagaries of international train travel at the moment I think I would choose the coach- may be less frequent and a bit slower (at 4 hrs and every 2 to 3 hours) but a walk up fare.

That's personal preference though. If you qualify a coach card brings that down to £23.30, which saving is effectively the annual cost of the card.

If you are going directly to Bath, my choice would be to bypass London. Take the train to Reading and switch to the train to Bath. Easy, one change, and with the train you can get up and stretch your legs. After a long flight, you will probably want to get up and stretch for awhile. Two and a half hours and you're there.

Because no one knows if your flight will be on time, or what the wait will be at Gatwick to clear immigration, I'd suggest getting an all day ticket. It costs more than an advanced but you won't worry if there are delays.

Given what we've just found out elsewhere, once cleared the airport see if you can get last minute advance fares. Close to midnight and still advance fares of £52.50 (£22.50 Gatwick to Reading, £30 Reading to Bath). On the first leg 1st class is only £7.50 more.
Supposed to be a deadline of 1800 the previous night on FGW but clearly not. Worth a try anyway.

I don't see any advantage whatsoever in going up to London, across London, just to get as GWR train back out of London.

If I were doing the trip it would be the direct train from Gatwick to Reading, change platforms and get the train from there to Bath. So much simpler. Simple is good. Simple and easy even better.

By the way, do book the Reading route as soon as you are clear of the airport- I am writing this at 0909, there are advance tickets on both trains on the Reading route still available all day- including on the 0929 Gatwick to Reading (so a cheap advance fare for a train in 20 minutes time!).
(and this morning heavy disruption on the Paddington to Reading line after a lineside fire yesterday with many GWR main line trains turning short at Reading)

... and presently the line between Guildford and Gatwick is blocked requiring travel via London!

Having done Reading to Gatwick many times the direct "North Downs" route is unquestionably preferable when everything is normal. Even then because it is only once an hour if I just miss it I would go via London rather than wait say 55 minutes. Thameslink & Elizabeth Line via Farringdon is probably the best way in that event now.

The OP hasn't given details of the full trip to advise whether returns or part-returns may make financial sense. If it is just Bath and London it is quite possible.

What this does show today is how well the rail industry pulls together when things go wrong, as Gatwick to Reading route specific tickets can be used, while the tunnel is blocked, via Thameslink and London Underground/Elizabeth Line to Paddington at no extra charge, or via the South Western Railway route from Reading and Waterloo/Clapham junction (a route not often talked about)

Indeed in the past I have travelled via London from Gatwick supported only by a tweet from GWR in response to one of mine. One general point is that GWR has no presence at Gatwick Airport station so the staff there are not always up-to-date with acceptances for any GWR issues and the queues for customer service are in any event usually very long.

Thanks so much all for the advice!