There are no direct trains between Bath & Moreton-in-Marsh (MIM). This means that you have to switch trains en-route and this is no big deal although obviously not as convenient as having a direct service. Another reason that you are getting high fares is because doing this journey is cheaper if you actually split the ticket into different legs. The following website will work this out for you but will take a commission of 15% of the amount saved:> https://trainsplit.com
If you were to buy an Advance ticket - that would only only be available on that specific train & date - with no refunds - although if an earlier train in the journey was cancelled/late, you would have the right to use a later train on the next ‘leg’ - just tell the guard what has happened. However, some trains have lower prices when/ if they are off peak and the above website shows you which ones these are. You can buy such tickets on the day - providing you know which trains are off peak - which the above website will tell you if you click PROCEED - even if not buying through them.
You can get by train from Bath to MIM in 2 ways. One is to go east (on a London bound train) to Didcot Parkway where you change for another train to Oxford and then change again for MIM. (Some options will tell you to go to Reading but these tend to be more expensive). The other option is to go west the short distance to Bristol Temple Meads where you change for a Cross Country Express to Cheltenham and then change again for Worcester Parkway - where you change again for MIM. (Going this way, some options will say take a train from Bath to Gloucester and then change for a train to Worcester Parkway). You just need to following the instructions for whichever route you take. If the change is at Cheltenham - it will be on the same platform. If at Worcester Parkway - you will need to take the lift to the higher level platform for the change to the other line.
The Cotswolds actually extend south to Bath although most of the ‘better’ villages tend to be at the northern end of The Cotswolds. US citizens on this forum frequently mention Mad Max tours out of Bath as being very good and they do day trips to some of the villages. Having said that, they seem to have improved the normal bus services in northern Cotswolds recently with Pullhams being the main company. They do, for example run a service (801) from Cheltenham to many of the attractive villages - but, I think you would have to take a local bus first the 1 mile from the station to the town centre to get the Pullhams service.
https://www.pulhams.co.uk/busservices/timetables/
It might be worth you getting a Friends & Family Railcard but note the 9.30 rule for weekdays. https://www.nationalrail.co.uk/railcards/
PS. It would have been better if you had put this query in the England forum rather than under general transportation.