Transfer from Stratford-upon-Avon to Moreton-in-Marsh without a car

We (4 adults) will need to travel from SuA to MiM in the afternoon of Thursday, May 30. We have 3 nights in MiM before heading to Oxford, should that be relevant to my question. We will not have a car. I have looked at the trains, which are currently just under £100 pp, which seems a bit high to me, but I understand that it is an awkward route. In spite of looking at the schedules, I am less certain that I understand the bus system, but am wondering if this might be a better option?