You will find the train times here:> www.nationalrail.co.uk
Just put in for PAD > BTH
The trains are usually very 30 minutes and travel at up to 125mph. Buying tickets on the day can be expensive - the cheapest deals for specific trains can be found about 11 weeks out. If you don’t want to be tied down to specific trains, check out the prices for Anytime returns or Off peak returns.
You can pick up Advance singles for £10 each way on specific trains if pre-booked well ahead. The train company is Great Western Railway but Americans have reported problems with their website. I suggest that you try and pre-book withhttps://www.crosscountrytrains.co.uk as they will let you change arrangements without a re-booking fee. (Yes, I know they are a different company but all train companies will sell each others tickets without a fee). You will get a booking number which you use to collect your tickets from a machine - using the SAME DEBIT card on which you made the booking.
Walk on returns are mainly £73.30 if paying on the day. On weekdays, if you travel on the 10.30am or later, this drops to £57.50 = off peak return. However, I have a way in which you can get this down to £48.10 return pay on the day. You walk into Paddington station and ask for an off-peak return to Didcot = £25.60. (On weekdays, you can travel on the 10am or later). Now, this 10am train is going to Paignton in Devon calling at Didcot, Swindon & Bath en-route so you will sit on the same train throughout. You then ask for an off peak return from Didcot to Swindon = £11.20. You then ask for an off peak return Swindon to Bath = £11.30. So we have a total of £48.10. Sounds bonkers but that is the crazy pricing for trains in Britain. If doing the 3 way split, you must make sure that your train stops at Didcot. (They all stop at Swindon). The x43 departures from Bath do stop at Didcot. You can check on the national rail website by clicking details > show calling points.
Do not travel on a Sunday as much engineering work is taking place on this route and this can lead to Sunday diversions. You will find more off peak fares for earlier departures on Saturdays.