Easiest, and cheapest way to go by bus or train between London/ Gatwick and Bath

You can either get a train with one change at Reading, or two changes at Farringdon and London Paddington. The one with two changes is relatively cheap, you can book in advance for about £30. The service with one change is £77. You can also get a bus with a change at Heathrow even cheaper, however this is very slow. Either flixbus or National express operate the bus service.

By splitting fares you can easily get a train via Reading for around £50. That means buying one ticket from Gatwick to Reading and another from Reading to Bath. Still a bit more than going through central London but more convenient especially if you’re coming off an overnight flight.

I would take the bus https://www.nationalexpress.com/en about 4.5 hours £30 ish - one change at LHR

The problem with taking the bus via Heathrow is that there are so few of them between Heathrow and Bath direct- every 2 to 3 hours.

The bus is £35 turn up and go fare.

The trick with splitting the tickets on the one change route is to avoid catching a train from Reading on a weekday between 4 and 7pm.

If you can avoid that then there is a train every 30 minutes- the fare should be £43.10 split as Gatwick to Reigate Off Peak Day Single £2.80,
Reigate to Bath Spa Super Off Peak Day Single £40.30 (Restriction Code YU- hot valid from Reading after 15:29 and before 19:01 on weekdays).
For travel from Reading between 15:29 and 17:03 you want a Off Peak Day Single Reigate to Bath at £54.50 (as opposed to £40.30). Total £57.30

The peak fare is just crazy, on GWR.

If you had to travel in the weekday peak you would take a Southern Train to Clapham Junction (£9 paying by contactless) then an Anytime Day Single on a South Western Railway train to Salisbury, changing for Bath- £51.50 , Total £60.50